A CAT Algebra question from Functions that appears in the Quantitative Aptitude section of the CAT Exam consists of concepts from Algebra. Types of functions, Compound function, Greatest integer functions and domain and range of a function all appear in Functions. In CAT Exam, one can generally expect to get 1~2 questions from Functions. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.
How many onto functions can be defined from the set A = {1, 2, 3, 4} to {a, b, c}?
Find the maximum value of f(x); if f(x) is defined as the Min {-(x – 1)^{2} + 2, (x – 2)^{2} + 1}
Consider functions f(x) = x^{2} + 2x, g(x) = and h(x) = g(f(x)). What are the domain and range of h(x)?
[x] = greatest integer less than or equal to x. If x lies between 3 and 5, 5 inclusive, what is the probability that [x^{2}] = [x]^{2}?
Give the domain and range of the following functions:
How many elements are present in the domain of ^{9–x}C_{x+1}?
f(x + y) = f(x)f(y) for all x, y, f(4) = + 3 what is f(–8)?
If f(x – 3) = 2x^{3 } + p – qx and f(x^{2 } – 4) = x^{2 } – 8q + 6p, then what is the value of p – q?
Given that x is real and f(x) = f(x + 1) + f(x – 1). Determine the value of ‘a’ that will satisfy f(x) + f(x + a) = 0?
x is a real number such that f(x) = 1/x when x > 0 and f(x) = 1/(x + 1) otherwise. Also f^{n}(x) = f(f^{n - 1 }(x)). What is f(3) + f^{2}(-3) + f^{3}(3) + f^{4}(-3)?
Which of the following functions are identical? f(x) = \\frac{x^3}{x^2}\\)
g(x) = (√x)^{2}
h(x) = x
The value of f∘g∘h(9) could be, if
f(x) = \\frac{1}{x}\\)
g(x) = \\frac{1}{(x-2)}\\)
h(x) = √x
For this question, assume the following operators: A*B = A^{2} - B^{2}
A-B = \\frac{A}{B}\\)
A+B = A * B
\\frac{A}{B}\\) = A+B
Which of the following expression would yield the result as x subtracted by y?
Find the domain of: \\frac{1}{(1-log (9-x))}\\) + √(x+1)?
If [X] – Greatest integer less than or equal to x. Find the value of
[√1] + [√2] + [√3] +……………………………………………………+ [√100]
Find the value of x for which x[x] = 39
Find the value of x for which x[x] = 15
If f(x) = \\frac{1}{g(x)}\\), then which of the following is correct?
If f(x) = \\frac{(x + 6)}{(x+2)}\\). Find the value of x for which f(x) = f^{-1}(x)?
If f(x) = |x| + |x+3| + |x+6| + ……………………………..+ |x+3t|, where x is an integer and t is a positive integer, find the minimum value of f(x) when t = 6
In the previous question if t = 7, for how many values of x, f(x) will be minimum?
If \\frac{f(x)}{f(x-1)}\\) = \\frac{(x-2)}{(x+1)}\\), for all x ≥ 0 and f(x) is a positive-valued function and f(6) = 81, find the value of f(4)
The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.
The minimum possible value of \(\frac{x^2-6 x+10}{3-x}\), for \(x\lt3\), is
Let \(r\) be a real number and \(f(x)=\left\{\begin{array}{cl}2 x-r & \text { if } x \geq r \\ r & \text { if } x\ lt r\end{array}\right.\). Then, the equation \(f(x)=f(f(x))\) holds for all real values of \(x\) where
Suppose for all integers \(x\), there are two functions \(f\) and \(g\) such that \(f(x)+f(x-1)-1=0\) and \(g(x)=x^2\). If \(f\left(x^2-x\right)=5\), then the value of the sum \(f(g(5))+g(f(5))\) is
Let \(f(x)\) be a quadratic polynomial in \(x\) such that \(f(x) \geq 0\) for all real numbers \(x\). If \(f(2)=0\) and \(f(4)=6\), then \(f(-2)\) is equal to
The largest real value of \(a\) for which the equation \(|x+a|+|x-1|=2\) has an infinite number of solutions for \(x\) is
For any real number \(x\), let \([x]\) be the largest integer less than or equal to \(x\). If \(\sum_{n=1}^N\left[\frac{1}{5}+\frac{n}{25}\right]=25\) then \(N\) is
Let \(0 \leq a \leq x \leq 100\) and \(f(x)=|x-a|+|x-100|+|x-a-50|\). Then the maximum value of \(f(x)\) becomes 100 when \(a\) is equal to
If \(f(x)=x^{2}-7 x\) and \(g(x)=x+3\), then the minimum value of \(f(g(x))-3 x\) is
For all real values of x, the range of the function f(x) = \(\frac{x^{2}+2 x+4}{2 x^{2}+4 x+9}\) is
f(x) = \(\frac{x^{2}+2 x-15}{x^{2}-7 x-18}\) is negative if and only if
If f(x+y) = f(x)f(y) and f(5) = 4, then f(10) - f(-10) is equal to
Let f(x) = x^{2} + ax + b and g(x) = f(x + 1) - f(x - 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is
If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is
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 [TITA]
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 [TITA]
Consider a function f(x+y) = f(x) f(y) where x , y are positive integers, and f(1) = 2. If f (a+1) + f (a+2) + ..... + f(a+n) = 16 (2^{n} - 1) then a is equal to. [TITA]
Let f(x)=max{5x, 52 - 2x^{2}}, where x is any positive real number.Then the minimum possible value of f(x) is (TITA)
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. [TITA]
Let f(x)=min{2x^{2}, 52 - 5x}, where x is any positive real number.Then the maximum possible value of f(x) is [TITA]
Let f(x) = x^{2} and g(x) = 2^{x}, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is
If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is [TITA]
Let f(x) = 2x – 5 and g(x) = 7 – 2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if
If f_{1}(x) = x^{2} + 11x + n and f_{2}(x) = x, then the largest positive integer n for which the equation f_{1}(x) = f_{2}(x) has two distinct real roots, is: (TITA)
If f(x) = \\frac{5x + 2}{3x - 5}) and g(x) = x^{2} – 2x – 1, then the value of g(f(f(3))) is:
The Questions that follow, are from actual XAT papers. If you wish to take them separately or plan to solve actual XAT papers at a later point in time, It would be a good idea to stop here.
If A ʘ B = (A + B) × B, then what is (5 ʘ 2) ʘ 5 ?
Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:
The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.
If minimum value of f(x) = x^{2} + 2bx + 2c^{2} is greater than the maximum value of g(x) = -x^{2} - 2cx + b^{2}, then for real value of x.
The set of all real numbers x for which x^{2} - |x + 2 |+ x > 0, is
The minimum value of f(x)=|3-x|+|2+x|+|5-x| is equal to __________.
If \\frac{1}{1^{2}}) + \\frac{1}{2^{2}}) + \\frac{1}{3^{2}}) + .... upto ∞ = \\frac{π^{2}}{6}), then the value of \\frac{1}{1^{2}}) + \\frac{1}{3^{2}}) + \\frac{1}{5^{2}}) + .... upto ∞ is
Given f(x) = x^{2} + log_{3}x and g(y) = 2y + f(y), then the value of g(3) equals
A real-valued function f satisfies the relation f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y, for all real numbers x and y, then the value of f(8) is
For all real values of x, \\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\) lies between 1 and k, and does not take any value above k. Then k equals
The maximum value of the natural number n for which 21^{n} divides 50! is
The function f(x) = \\frac{x^{3} - 5x^{2} - 8x}{3}\\) is
For a > b > c > 0, the minimum value of the function f(x) = |x - a| + |x - b| + |x - c| is
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