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Recent questions tagged functions

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41
CAT 2002 | Question: 68
If $f(x) = \log(1+x)/(1-x))$, then $f(x)+f(y)=$ $f(x+y)$ $f(1+xy)$ $(x+y) \: f(1+xy)$ $f (\frac{x+y}{1+xy})$
If $f(x) = \log(1+x)/(1-x))$, then $f(x)+f(y)=$$f(x+y)$$f(1+xy)$$(x+y) \: f(1+xy)$$f (\frac{x+y}{1+xy})$
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42
CAT 2003 | Question: 1-117
The function $f(x) = |x-2| + |2.5-x| + |3.6-x|$, where $x$ is a real number, attains a minimum at $x=2.3$ $x=2.5$ $x=2.7$ None of these
The function $f(x) = |x-2| + |2.5-x| + |3.6-x|$, where $x$ is a real number, attains a minimum at$x=2.3$$x=2.5$$x=2.7$None of these
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43
CAT 2014 | Question: 50
A quadratic function $ƒ(x)$ attains a maximum of $3$ at $x = 1$. The value of the function at $x = 0$ is $1$. What is the value $ƒ(x)$ at $x = 10$? $–119$ $–159$ $–110$ $–180$
A quadratic function $ƒ(x)$ attains a maximum of $3$ at $x = 1$. The value of the function at $x = 0$ is $1$. What is the value $ƒ(x)$ at $x = 10$? $–119$ $–159$ $�...
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1 answer
45
CAT 2014 | Question: 11
If $y = f(x)$ and $f(x) = (1 - x) / (1 + x)$, which of the following is true? $f(2x) = f(x) – 1$ $x = f(2y) - 1$ $f(1/x) = f(x)$ $x = f(y)$
If $y = f(x)$ and $f(x) = (1 - x) / (1 + x)$, which of the following is true? $f(2x) = f(x) – 1$ $x = f(2y) - 1$ $f(1/x) = f(x)$ $x = f(y)$
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1 answer
47
CAT 2004 | Question: 47
If $f(x) = x^3 - 4x + p$, and $f(0)$ and $f(1)$ are of opposite signs, then which of the following is necessarily true? $-1 < p < 2$ $0 < p < 3$ $-2 < p < 1$ $-3 < p < 0$
If $f(x) = x^3 - 4x + p$, and $f(0)$ and $f(1)$ are of opposite signs, then which of the following is necessarily true?$-1 < p < 2$$0 < p < 3$$-2 < p < 1$$-3 < p < 0$
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48
CAT 2005 | Question: 27
Let $g(x)$ be a function such that $g(x+1) +g(x-1) = g(x)$ for every real $x.$ Then for what value of $p$ is the relation $g(x+p)=g(x)$ necessarily true for every real $x?$ $5$ $3$ $2$ $6$
Let $g(x)$ be a function such that $g(x+1) +g(x-1) = g(x)$ for every real $x.$ Then for what value of $p$ is the relation $g(x+p)=g(x)$ necessarily true for every real $x...
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1 answer
49
CAT 2007 | Question: 25
A function $f(x) $ satisfies $f(1)=3600$ and $f(1)+f(2)+ \dots + f(n) = n^2 f(n)$, for all positive integers $n>1.$ What is the value of $f(9)?$ $80$ $240$ $200$ $100$ $120$
A function $f(x) $ satisfies $f(1)=3600$ and $f(1)+f(2)+ \dots + f(n) = n^2 f(n)$, for all positive integers $n>1.$ What is the value of $f(9)?$$80$$240$$200$$100$$120$
2 votes
1 answer
50
CAT 2008 | Question: 13
Let $f(x) $ be a function satisfying $f(x) f(y) =f(xy)$ for all real $x, y$. If $f(2)=4$, then what is the value of $f\left(\frac{1}{2}\right)$ $0$ $\frac{1}{4}$ $\frac{1}{2}$ $1$ cannot be determined
Let $f(x) $ be a function satisfying $f(x) f(y) =f(xy)$ for all real $x, y$. If $f(2)=4$, then what is the value of $f\left(\frac{1}{2}\right)$$0$$\frac{1}{4}$$\frac{1}{2...
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2 answers
51
If f(x) = minimum of (3x + 5, 10 - 2x), what is the maximum possible value of f(x)?
If f (x) = minimum of (3x + 5, 10 - 2x), what is the maximum possible value of f (x)?1368
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