Recent questions tagged functions

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1 answer
2
1 votes
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5
If $ f(x+y) = f(x) f(y) $ and $ f(5) = 4,$ then $ f(10) – f(-10) $ is equal to $0$$15.9375$$3$$14.0625$
2 votes
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6
Let $f(x) = x^{2} + ax + b $ and $g(x) = f(x+1) – f(x-1).$ If $ f(x) \geq 0 $ for all real $x,$ and $ g(20) = 72,$ then the smallest possible value of $b$ is $1$$16$$0$...
1 votes
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7
If $f\left ( 5+x \right )= f\left ( 5-x \right )$ for every real $x,$ and $f\left ( x \right )=0$ has four distinct real roots, then the sum of these roots is$0$$40$$10$$...
1 votes
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8
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 $...
2 votes
1 answer
9
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 ________
1 votes
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10
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...
1 votes
1 answer
11
1 votes
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12
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...
1 votes
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13
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$$2/3$
1 votes
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14
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15
1 votes
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16
For all non-negative integers $x$ and $y$, $f(x,y)$ is defined as below.$f( 0,y) = y+1$$f(x+1,0) = f( x, 1)$$f( x+1, y+1) = f\left( x,f( x+1,y) \right)$Then what is the v...
1 votes
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17
$\begin{array}{}Let\;f_{n+1}(x)&=f_n(x)+1\;\text{if $n$ is a multiple of 3}\\ &=f_n(x)-1\;\text{otherwise.}\end{array}$If $f_1(1)=0$, then what is $f_{50}(1)$?$-18$$-16$$...
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18
The graphs given alongside represent two functions $f(x)\:\text{and}\:g(x)$ respectively. Which of the following is true?$g(x)=[f(x)]$$g(x)=f(-x)$$g(x)=-f(x)$None of thes...
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19
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21
For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals ______...
1 votes
1 answer
22
Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to _...
1 votes
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23
If $g(x)=p\mid x \mid-qx^2$, where $p$ and $q$ are constants, then at $x=0, g(x)$ will bemaximum when $p>0,q>0$minimum when $p<0,q<0$minimum when $p>0,q<0$maximum when $p...
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28
Answer the following question based on the information given below.For real numbers $x, y,$ let$f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\...
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35
For all non-negative integers $x$ and $y, f(x, y)$ is defined as below$f(0, y) = y + 1$$f(x + 1, 0) = f(x, 1)$$f(x + 1,y + 1) = f(x, f(x + 1, y))$Then, what is the value ...