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Recent questions tagged functions
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CAT 2004 | Question: 62
Answer the questions on the basis of the information given below: $f_{1}(x) = \left\{\begin{matrix} x & 0 \leq x \leq 1 \\ 1 & x \geq 1 \\ 0 & \text{otherwise} \end{matrix}\right.$ $f_{2}(x) = f_{1}(-x) \;\; \text{for all} \; x $ ... $f_2(-x) = f_4(x) \: \text{for all }\;x$ $f_1(x) + f_3(x) = 0 \: \text{for all }\;x$
Lakshman Bhaiya
asked
in
Quantitative Aptitude
Mar 30, 2022
by
Lakshman Bhaiya
13.7k
points
213
views
cat2004
quantitative-aptitude
functions
1
vote
1
answer
2
CAT 2021 Set-3 | Quantitative Aptitude | Question: 12
If $f(x) = x^{2} – 7x$ and $g(x) = x + 3,$ then the minimum value of $f(g(x)) – 3x$ is $ -16$ $ -15$ $ -20$ $ -12$
soujanyareddy13
asked
in
Quantitative Aptitude
Jan 20, 2022
by
soujanyareddy13
2.7k
points
365
views
cat2021-set3
quantitative-aptitude
functions
1
vote
1
answer
3
CAT 2021 Set-2 | Quantitative Aptitude | Question: 15
For all real values of $x,$ the range of the function $f(x) = \dfrac{x^{2} + 2x + 4}{2x^{2} + 4x + 9}$ is $ \left(\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{8}{9} \right)$ $ \left[\frac{4}{9}, \frac{8}{9} \right]$
soujanyareddy13
asked
in
Quantitative Aptitude
Jan 20, 2022
by
soujanyareddy13
2.7k
points
340
views
cat2021-set2
quantitative-aptitude
functions
1
vote
1
answer
4
CAT 2021 Set-1 | Quantitative Aptitude | Question: 8
$f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$ is negative if and only if $ – 2 < x < 3 \; \text{or} \; x > 9 $ $ x < – 5 \; \text{or} \; 3 < x < 9 $ $ – 5 < x < – 2 \; \text{or} \; 3 < x < 9 $ $ x < – 5 \; \text{or} \; – 2 < x < 3 $
soujanyareddy13
asked
in
Quantitative Aptitude
Jan 19, 2022
by
soujanyareddy13
2.7k
points
482
views
cat2021-set1
quantitative-aptitude
functions
1
vote
1
answer
5
CAT 2020 Set-3 | Question: 58
If $ f(x+y) = f(x) f(y) $ and $ f(5) = 4,$ then $ f(10) – f(-10) $ is equal to $0$ $15.9375$ $3$ $14.0625$
soujanyareddy13
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in
Quantitative Aptitude
Sep 17, 2021
by
soujanyareddy13
2.7k
points
423
views
cat2020-set3
quantitative-aptitude
functions
2
votes
1
answer
6
CAT 2020 Set-2 | Question: 72
Let $f(x) = x^{2} + ax + b $ and $g(x) = f(x+1) – f(x-1).$ If $ f(x) \geq 0 $ for all real $x,$ and $ g(20) = 72,$ then the smallest possible value of $b$ is $1$ $16$ $0$ $4$
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 17, 2021
by
soujanyareddy13
2.7k
points
476
views
cat2020-set2
quantitative-aptitude
functions
1
vote
1
answer
7
CAT 2020 Set-1 | Question: 68
If $f\left ( 5+x \right )= f\left ( 5-x \right )$ for every real $x,$ and $f\left ( x \right )=0$ has four distinct real roots, then the sum of these roots is $0$ $40$ $10$ $20$
soujanyareddy13
asked
in
Quantitative Aptitude
Sep 16, 2021
by
soujanyareddy13
2.7k
points
447
views
cat2020-set1
quantitative-aptitude
functions
1
vote
1
answer
8
CAT 2019 Set-2 | Question: 95
Let $f$ be a function such that $f (mn) = f (m) f (n)$ for every positive integers $m$ and $n$. If $f (1), f (2)$ and $f (3)$ are positive integers, $f (1) < f (2),$ and $f (24) = 54$, then $f (18)$ equals _______
go_editor
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in
Quantitative Aptitude
Mar 20, 2020
by
go_editor
13.8k
points
594
views
cat2019-2
quantitative-aptitude
functions
numerical-answer
2
votes
1
answer
9
CAT 2018 Set-1 | Question: 93
If $f(x+2)=f(x)+f(x+1)$ for all positive integers $x$, and $f(11)=91,f(15)=617$, then $f(10)$ equals ________
go_editor
asked
in
Quantitative Aptitude
Mar 20, 2020
by
go_editor
13.8k
points
535
views
cat2018-1
quantitative-aptitude
functions
numerical-answer
1
vote
1
answer
10
CAT 2017 Set-2 | Question: 89
Let $f\left ( x \right )=x^{2}$ and $g\left ( x \right )=2^{x}$, for all real $x$. Then the value of $ f \left ( f\left ( g\left ( x \right ) \right )+g\left( f\left ( x \right ) \right ) \right)$ at $x=1$ is $16$ $18$ $36$ $40$
go_editor
asked
in
Quantitative Aptitude
Mar 16, 2020
by
go_editor
13.8k
points
458
views
cat2017-2
quantitative-aptitude
functions
1
vote
1
answer
11
CAT 2017 Set-2 | Question: 98
Let $f\left ( x \right )=2x-5$ and $g\left ( x \right )=7-2x.$ Then $ \mid f\left ( x \right ) + g\left ( x \right ) \mid=\mid f(x) \mid + \mid g\left ( x \right ) \mid$ if and only if $5/2<x<7/2$ $x\leq 5/2$ or $x\geq 7/2$ $x< 5/2$ or $x\geq 7/2$ $5/2\leq x\leq 7/2$
go_editor
asked
in
Quantitative Aptitude
Mar 16, 2020
by
go_editor
13.8k
points
611
views
cat2017-2
quantitative-aptitude
functions
1
vote
1
answer
12
CAT 2017 Set-2 | Question: 97
If $f\left ( ab \right )=f\left ( a \right )f\left ( b \right )$ for all positive integers $a$ and $b$, then the largest possible value of $f\left (1\right )$ is $1$ $2$ $0$ $3$
go_editor
asked
in
Quantitative Aptitude
Mar 16, 2020
by
go_editor
13.8k
points
436
views
cat2017-2
quantitative-aptitude
functions
1
vote
1
answer
13
CAT 2017 Set-1 | Question: 99
If $f( x)=\dfrac{5x+2}{ 3x-5}$ and $g( x )=x^{2}-2x-1,$ then the value of $g( f( f( 3 ) ) )$ is $2$ $1/3$ $6$ $2/3$
go_editor
asked
in
Quantitative Aptitude
Mar 13, 2020
by
go_editor
13.8k
points
591
views
cat2017-1
quantitative-aptitude
functions
1
vote
1
answer
14
CAT 2016 | Question: 73
$A, S, M$ and $D$ are functions of $x$ and $y$, and they are defined as follows. $A(x, y) = x + y$ $M(x, y) = xy$ $S(x,y)= x-y$ $D(x,y)= x/y, y\neq 0$ What is the value of $M(M(A(M(x, y), S(y, x)), x), A(y, x))$ for $x = 2, y = 3$? $60$ $140$ $25$ $70$
go_editor
asked
in
Quantitative Aptitude
Mar 11, 2020
by
go_editor
13.8k
points
682
views
cat2016
quantitative-aptitude
functions
0
votes
0
answers
15
CAT 2015 | Question: 81
The set of all positive integers is the union of two disjoint subsets$:\left \{ f\left ( 1 \right ),f\left ( 2 \right ), \dots, f\left ( n \right ), \dots \right \}$ ... $n \geq 1$. What is the value of $g\left ( 1 \right )?$ $0$ $2$ $1$ Cannot be determined
go_editor
asked
in
Quantitative Aptitude
Mar 9, 2020
by
go_editor
13.8k
points
467
views
cat2015
quantitative-aptitude
functions
1
vote
1
answer
16
CAT 2015 | Question: 82
For all non-negative integers $x$ and $y$, $f(x,y)$ is defined as below. $f( 0,y) = y+1$ $f(x+1,0) = f( x, 1)$ $f( x+1, y+1) = f\left( x,f( x+1,y) \right)$ Then what is the value of $f(1,2)$ ________
go_editor
asked
in
Quantitative Aptitude
Mar 9, 2020
by
go_editor
13.8k
points
2.5k
views
cat2015
quantitative-aptitude
functions
numerical-answer
1
vote
1
answer
17
CAT 2011 | Question: 4
$\begin{array}{}Let\;f_{n+1}(x)&=f_n(x)+1\;\text{if $n$ is a multiple of 3}\\ &=f_n(x)-1\;\text{otherwise.}\end{array}$ If $f_1(1)=0$, then what is $f_{50}(1)$? $-18$ $-16$ $-17$ Cannot be determined
Krithiga2101
asked
in
Quantitative Aptitude
Mar 9, 2020
by
Krithiga2101
298
points
800
views
cat2011
quantitative-aptitude
functions
0
votes
0
answers
18
CAT 2011 | Question: 17
The graphs given alongside represent two functions $f(x)\:\text{and}\:g(x)$ respectively. Which of the following is true? $g(x)=[f(x)]$ $g(x)=f(-x)$ $g(x)=-f(x)$ None of these
Krithiga2101
asked
in
Quantitative Aptitude
Mar 9, 2020
by
Krithiga2101
298
points
518
views
cat2011
quantitative-aptitude
functions
0
votes
0
answers
19
CAT 2011 | Question: 20
Consider the function given by $f(x) =\mid x-1\mid-x$ What is the area of the triangle bounded by the graph of the given function with the coordinate axis given by $x=0\:\text{and}\:y=0$? $2$ $\large\frac{1}{4}$ $\large\frac{1}{2}$ $1$
Krithiga2101
asked
in
Quantitative Aptitude
Mar 9, 2020
by
Krithiga2101
298
points
643
views
cat2011
quantitative-aptitude
functions
area
0
votes
0
answers
20
CAT 2011 | Question: 21
Consider the function given by $f(x) =\mid x-1\mid-x$ Which of the following is not true about the graph of $f(x)$? A portion of the graph is parallel to the line $y = 25$. A portion of graph is in 2nd quadrant. Some portion of graph lies in 1st quadrant. Some portion of graph lies in 3rd quadrant.
Krithiga2101
asked
in
Quantitative Aptitude
Mar 9, 2020
by
Krithiga2101
298
points
427
views
cat2011
quantitative-aptitude
functions
1
vote
1
answer
21
CAT 2019 Set-1 | Question: 87
For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals _______
go_editor
asked
in
Quantitative Aptitude
Mar 8, 2020
by
go_editor
13.8k
points
693
views
cat2019-1
quantitative-aptitude
functions
numerical-answer
1
vote
1
answer
22
CAT 2019 Set-1 | Question: 90
Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to ______
go_editor
asked
in
Quantitative Aptitude
Mar 8, 2020
by
go_editor
13.8k
points
491
views
cat2019-1
quantitative-aptitude
functions
numerical-answer
1
vote
0
answers
23
CAT 2013 | Question: 23
If $g(x)=p\mid x \mid-qx^2$, where $p$ and $q$ are constants, then at $x=0, g(x)$ will be maximum when $p>0,q>0$ minimum when $p<0,q<0$ minimum when $p>0,q<0$ maximum when $p>0,q<0$
admin
asked
in
Quantitative Aptitude
Mar 6, 2020
by
admin
3.7k
points
513
views
cat2013
quantitative-aptitude
functions
0
votes
0
answers
24
CAT 2013 | Question: 29
Let $f(x)= \dfrac{1}{1+x^2}$ and $g(x)=\dfrac{e^{−x}}{1+[x]}$, where $[x]$ is the greatest integer less than or equal to $x$. Then which of the following domain is true? domain of $(f+g)=R-(-2,-1]$ domain of $(f+g)=R-[-1,0)$ ... Both II and IV Both I and III Both I and IV Both II and III
admin
asked
in
Quantitative Aptitude
Mar 6, 2020
by
admin
3.7k
points
449
views
cat2013
quantitative-aptitude
functions
0
votes
0
answers
25
CAT 2010 | Question: 16
Let $f$ be an injective map with domain $\left \{ x, y, z \right \}$ and the range $\left \{ 1, 2, 3 \right \}$ such that exactly one of the following statements is correct and the remaining are false. $f\left \{x \right \}=1,f\left ( y \right )\neq 1,f\left ( z \right )\neq 2.$ The value of $f^{-1}\left ( 1 \right )$ is $x$ $y$ $z$ None of the above
Arjun
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in
Quantitative Aptitude
Mar 1, 2020
by
Arjun
8.6k
points
421
views
cat2010
quantitative-aptitude
functions
0
votes
1
answer
26
CAT 1999 | Question: 100
Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following expressions yields $x^2$ as a result? $F(f(x, -x)).G(f(x, -x))$ $F(f(x, x)).G(f(x, x)).4$ $-F(f(x, x)).G(f(x, -x)) \: \log_2 16$ $f(x,x).f(x,x)$
go_editor
asked
in
Logical Reasoning
May 14, 2016
by
go_editor
13.8k
points
500
views
cat1999
logical-reasoning
functions
0
votes
1
answer
27
CAT 1999 | Question: 98
Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following statements is true? $F(f(x,y)) .G(f(x,y)) = -F(f(x,y)).G(f(x,y))$ ... $F(f(x,y)) .G(f(x,y)) \neq G(f(x,y)).F(f(x,y))$ $F(f(x,y)) +G(f(x,y)) + f(x,y)= f(-x,-y)$
go_editor
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Logical Reasoning
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by
go_editor
13.8k
points
615
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cat1999
logical-reasoning
functions
0
votes
0
answers
28
CAT 2000 | Question: 76
Answer the following question based on the information given below. For real numbers $x, y,$ ... $x$ and $y$ are less than $-1$ Both $x$ and $y$ are positive Both $x$ and $y$ are negative $y > x$
go_editor
asked
in
Quantitative Aptitude
May 1, 2016
by
go_editor
13.8k
points
727
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cat2000
quantitative-aptitude
functions
0
votes
0
answers
29
CAT 2000 | Question: 79
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ ... $(h(x, y, z) - f(x, y, z))/(n(x, y, z) - g(x, y, z))$
go_editor
asked
in
Quantitative Aptitude
May 1, 2016
by
go_editor
13.8k
points
438
views
cat2000
quantitative-aptitude
functions
0
votes
1
answer
30
CAT 2000 | Question: 78
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ ... $(j(x, y, z) - g(x, y, z))/h(x, y, z)$ $(f(x, y, z) - h(x, y, z))/f(x, y, z)$
go_editor
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in
Quantitative Aptitude
May 1, 2016
by
go_editor
13.8k
points
1.1k
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cat2000
quantitative-aptitude
functions
1
vote
1
answer
31
CAT 2014 | Question: 33
Use the following information for next two questions: A function $f(x)$ is said to be even if $f(-x) = f(x)$, and odd if $f(-x) = -f(x)$. Thus, for example, the function given by $f(x)=x^{2}$ is even, while the ... questions. The sum of two odd functions is always an even function is always an odd function is sometimes odd and sometimes even may be neither odd nor even
go_editor
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in
Quantitative Aptitude
Apr 27, 2016
by
go_editor
13.8k
points
680
views
cat2014
quantitative-aptitude
functions
0
votes
0
answers
32
CAT 2000 | Question: 88
Answer the following question based on the information given below. For a real number $x,$ let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... $r$ is an integer $\geq 2.$ Then what is the value of $f^{r-1}(-r) + f^r(-r)+f^{r+1}(-r)$? $-1$ $0$ $1$ None of these
go_editor
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in
Quantitative Aptitude
Apr 25, 2016
by
go_editor
13.8k
points
338
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cat2000
quantitative-aptitude
functions
0
votes
0
answers
33
CAT 2000 | Question: 84
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$
go_editor
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in
Quantitative Aptitude
Apr 25, 2016
by
go_editor
13.8k
points
468
views
cat2000
quantitative-aptitude
functions
0
votes
0
answers
34
CAT 2000 | Question: 83
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$
go_editor
asked
in
Quantitative Aptitude
Apr 25, 2016
by
go_editor
13.8k
points
495
views
cat2000
quantitative-aptitude
functions
0
votes
0
answers
35
CAT 2000 | Question: 107
For all non-negative integers $x$ and $y, f(x, y)$ is defined as below $f(0, y) = y + 1$ $f(x + 1, 0) = f(x, 1)$ $f(x + 1,y + 1) = f(x, f(x + 1, y))$ Then, what is the value of $f(1, 2)?$ Two Four Three Cannot be determined
go_editor
asked
in
Quantitative Aptitude
Mar 30, 2016
by
go_editor
13.8k
points
540
views
cat2000
quantitative-aptitude
functions
0
votes
0
answers
36
CAT 2000 | Question: 105
The set of all positive integers is the union of two disjoint subsets $\{f(1), f(2),\dots ,f(n),\dots\}$ and $\{g(1), g(2),\dots,g(n),\dots\},$ where $f(1) < f(2) <\dots < f(n) < \dots,$ and $g(1) < g(2) <\dots< g(n) < \dots,$ and $g(n) = f(f(n)) + 1$ for all $n \geq 1.$ What is the value of $g(1)?$ Zero Two One Cannot be determined
go_editor
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in
Quantitative Aptitude
Mar 30, 2016
by
go_editor
13.8k
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855
views
cat2000
quantitative-aptitude
functions
0
votes
0
answers
37
CAT 2000 | Question: 87
Answer the following question based on the information given below. For a real number $x$, let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... What is the value of the product, $f(2)f^2(2)f^3(2)f^4(2)f^5(2)$? $\frac{1}{3}$ $3$ $\frac{1}{18}$ None of these
go_editor
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Quantitative Aptitude
Mar 29, 2016
by
go_editor
13.8k
points
300
views
cat2000
quantitative-aptitude
functions
0
votes
0
answers
38
CAT 2000 | Question: 82
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$
go_editor
asked
in
Quantitative Aptitude
Mar 29, 2016
by
go_editor
13.8k
points
309
views
cat2000
quantitative-aptitude
functions
0
votes
0
answers
39
CAT 2000 | Question: 77
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ ... $f(x, y, z)/g(x, y, z)$ $(f(x, y, z) + h(x, y, z) - g(x, y, z))/j(x, y, z)$
go_editor
asked
in
Quantitative Aptitude
Mar 29, 2016
by
go_editor
13.8k
points
332
views
cat2000
quantitative-aptitude
functions
0
votes
0
answers
40
CAT 2000 | Question: 75
Answer the following question based on the information given below. For real numbers $x, y,$ let $f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\;\text{if}\; (x + y)^{0.5}\;\text{is real} \\ (x + y)^2,\;\text{otherwise} \end{matrix}\right.$ ... $f(x, y) - (g(x, y))^2$ $g(x, y) - (f(x, y))^2$ $f(x, y) + g(x, y)$
go_editor
asked
in
Quantitative Aptitude
Mar 29, 2016
by
go_editor
13.8k
points
385
views
cat2000
quantitative-aptitude
functions
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