CAT Questions | CAT Algebra Questions

CAT Quantitative Aptitude | CAT Algebra: Functions Questions

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.

  1. CAT Functions - Onto Functions

    How many onto functions can be defined from the set A = {1, 2, 3, 4} to {a, b, c}?

    1. 81
    2. 79
    3. 36
    4. 45
    Choice C
    36

  2. CAT Functions - Quadratic Expressions

    Find the maximum value of f(x); if f(x) is defined as the Min {-(x – 1)2 + 2, (x – 2)2 + 1}

    1. 1
    2. 2
    3. 0
    4. 3
    Choice B
    2

  3. CAT Functions - Compound functions

    Consider functions f(x) = x2 + 2x, g(x) = and h(x) = g(f(x)). What are the domain and range of h(x)?

    Domain: ( -∞, +∞), Range -[0, ∞]

  4. CAT Functions - Greatest Integer Function

    [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?

    1. Roughly 0.64
    2. Roughly 0.5
    3. Roughly 0.14
    4. Roughly 0.36
    Choice C
    Roughly 0.14

  5. CAT Functions - Domain and Range

    Give the domain and range of the following functions:

    1. f(x) = x2 + 1
    2. g(x) = log(x + 1)
    3. h(x) = 2x
    4. f(x) = 1/(x+1)
    5. p(x) = |x + 1|
    6. q(x) = [2x], where [x] gives the greatest integer less than or equal to x

  6. CAT Functions - Domain and Range

    How many elements are present in the domain of 9–xCx+1?

    1. 5
    2. 6
    3. 4
    4. 7
    Choice B
    6

  7. CAT Functions - Unconventional Question

    f(x + y) = f(x)f(y) for all x, y, f(4) = + 3 what is f(–8)?

    1. 1/3
    2. 1/9
    3. 9
    4. 6
    Choice B
    1/9

  8. CAT Functions - Value of p - q

    If f(x – 3) = 2x3 + p – qx and f(x2 – 4) = x2 – 8q + 6p, then what is the value of p – q?

    1. 5
    2. 10
    3. 6
    4. Cannot determine
    Choice B
    10

  9. CAT Functions - Value of a

    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?

    1. -1
    2. -2
    3. 1
    4. 3
    Choice D
    3

  10. CAT Functions - Function of a function

    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)?

    1. -2/3
    2. 14/3
    3. 0
    4. 3
    Choice B
    14/3

  11. CAT Functions - Identical Functions

    Which of the following functions are identical? f(x) = \\frac{x^3}{x^2}\\)
    g(x) = (√x)2
    h(x) = x

    1. f(x) and g(x)
    2. f(x) and h(x)
    3. All 3 are identical
    4. None of these are identical
    Choice D
    None of these are identical

  12. CAT Functions - Function of a function

    The value of f∘g∘h(9) could be, if
    f(x) = \\frac{1}{x}\\)
    g(x) = \\frac{1}{(x-2)}\\)
    h(x) = √x

    1. 3
    2. \\frac{1}{3}\\)
    3. -5
    4. None of these
    Choice D
    None of these

  13. CAT Functions - Function of a function

    For this question, assume the following operators: A*B = A2 - B2
    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?

    1. (x*y)-(x+5)
    2. (\\frac{x}{y}\\))*(x-y)
    3. (x*y) - (\\frac{x}{y}\\))
    4. (x+y)*(x-y)
    Choice C
    (x*y) - (\\frac{x}{y}\\))

  14. CAT Functions - Domain of Function

    Find the domain of: \\frac{1}{(1-log (9-x))}\\) + √(x+1)?

    1. (-∞,9)
    2. [-1,9)
    3. [-1,9) excluding 0
    4. (-1,9)
    Choice D
    (-1,9)

  15. CAT Functions - Value of a Sequence

    If [X] – Greatest integer less than or equal to x. Find the value of
    [√1] + [√2] + [√3] +……………………………………………………+ [√100]

    1. 615
    2. 625
    3. 5050
    4. 505
    Choice B
    625

  16. CAT Functions - Greatest Integer Function

    Find the value of x for which x[x] = 39

    1. 6.244
    2. 6.2
    3. 6.3
    4. 6.5
    Choice D
    6.5

  17. CAT Functions - Greatest Integer Function

    Find the value of x for which x[x] = 15

    1. 3.5
    2. 5
    3. 6.1
    4. None of these
    Choice D
    None of these

  18. CAT Functions - Composite Function

    If f(x) = \\frac{1}{g(x)}\\), then which of the following is correct?

    1. f(f(g(g(f(x))))) = g(f(g(g(g(x)))))
    2. f(f(f(g(g(g(f(g(x)))))))) = g(g(g(g(f(g(f(f(x))))))))
    3. f(f(g(f(x)))) = g(g(f(g(x))))
    4. 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))))))))

  19. CAT Functions - Invertible Functions

    If f(x) = \\frac{(x + 6)}{(x+2)}\\). Find the value of x for which f(x) = f-1(x)?

    1. -3
    2. 2
    3. Both A and B
    4. None of these
    Choice C
    Both A and B

  20. CAT Functions - Minimum Value of f(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

    1. 63
    2. 36
    3. 30
    4. 25
    Choice B
    36

  21. CAT Functions - Minimum Value of f(x)

    In the previous question if t = 7, for how many values of x, f(x) will be minimum?

    1. 1
    2. 2
    3. 4
    4. 8
    Choice C
    4

  22. CAT Functions - Value of a Sequence

    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, f(2) = 4, find the value of f(4)

    1. 8
    2. 18
    3. 25
    4. 28
    Choice B
    18

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