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} ?
A. 81
B. 79
C. 36
D. 45
Choice C
36
Find the maximum value of f(x); if f(x) is defined as the Min {-(x – 1)2 + 2, (x – 2)2 + 1}
A. 1
B. 2
C. 0
D. 3
Choice B
2
Consider functions f(x) = x2 + 2x, g(x) =
Domain: ( -∞, +∞), Range -[0, ∞]
[x] = greatest integer less than or equal to x. If x lies between 3 and 5, 5 inclusive, what is the probability that [x2] = [x]2?
A. Roughly 0.64
B. Roughly 0.5
C. Roughly 0.14
D. Roughly 0.36
Choice C
Roughly 0.14
Give the domain and range of the following functions:
A. f(x) = x2 + 1
B. g(x) = log(x + 1)
C. h(x) = 2x
D. f(x) = 1/(x+1)
E. p(x) = |x + 1|
F. q(x) = [2x], where [x] gives the greatest integer less than or equal to x
How many elements are present in the domain of 9–xCx+1?
A. 5
B. 6
C. 4
D. 7
Choice B
6
f(x + y) = f(x)f(y) for all x, y, f(4) = + 3 what is f(–8)?
A. 1/3
B. 1/9
C. 9
D. 6
Choice B
1/9
If f(x – 3) = 2x3 + p – qx and f(x2 – 4) = x2 – 8q + 6p, then what is the value of p – q?
A. 5
B. 10
C. 6
D. Cannot determine
Choice B
10
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?
A. -1
B. -2
C. 1
D. 3
Choice D
3
x is a real number such that f(x) = 1/x when x > 0 and f(x) = 1/(x + 1) otherwise. Also fn(x) = f(fn - 1 (x)). What is f(3) + f2(-3) + f3(3) + f4(-3)?
A. -(2/3)
B. 14/3
C. 0
D. 3
Choice B
14/3
Which of the following functions are identical? f(x) =
g(x) = (√x)2
h(x) = x
A. f(x) and g(x)
B. f(x) and h(x)
C. All 3 are identical
D. None of these are identical
Choice D
None of these are identical
The value of f∘g∘h(9) could be, if
f(x) =
g(x) =
h(x) = √x
A. 3
B.
C. -5
D. None of these
Choice D
None of these
For this question, assume the following operators: A × B = A2 - B2
A - B =
A + B = A × B
Which of the following expression would yield the result as x subtracted by y?
A. (x × y) - (x + 5)
B.
C. (x × y) - (
D. (x + y) × (x - y)
Choice C
(x*y) - (x⁄y)
Find the domain of
A. (-∞,9)
B. [-1,9)
C. [-1,9) excluding 0
D. (-1,9)
Choice D
(-1,9)
If [X] – Greatest integer less than or equal to x. Find the value of
[√1] + [√2] + [√3] +...........+ [√100]
A. 615
B. 625
C. 5050
D. 505
Choice B
625
Find the value of x for which x[x] = 39
A. 6.244
B. 6.2
C. 6.3
D. 6.5
Choice D
6.5
Find the value of x for which x[x] = 15
A. 3.5
B. 5
C. 6.1
D. None of these
Choice D
None of these
If f(x) =
A. f(f(g(g(f(x))))) = g(f(g(g(g(x)))))
B. f(f(f(g(g(g(f(g(x)))))))) = g(g(g(g(f(g(f(f(x))))))))
C. f(f(g(f(x)))) = g(g(f(g(x))))
D. f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))
Choice D
f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))
If f(x) =
A. -3
B. 2
C. Both A and B
D. None of these
Choice C
Both A and B
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
A. 63
B. 36
C. 30
D. 25
Choice B
36
In the previous question if t = 7, for how many values of x, f(x) will be minimum?
A. 1
B. 2
C. 4
D. 8
Choice C
4
If
A. 8
B. 18
C. 25
D. 28
Choice B
18
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