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, find the value of f(4)

    1. 8
    2. 283.5
    3. 25
    4. 28
    Choice B
    283.5

  23. The following questions are from IPMAT Rohtak and Indore sample papers. If you want to take these questions as a mock please click below.

    IPMAT Rohtak Sample Paper Mock
    IPMAT Indore Sample Paper Mock

    Please note that the explanation button will take you to the IPMAT solution page.


  24. IPMAT 2020 Sample Paper - IPM Rohtak Quants,Functions

    If minimum value of f(x) = x2 + 2bx + 2c2 is greater than the maximum value of g(x) = -x2 - 2cx + b2, then for real value of x.

    1. |c| > √2|b|
    2. √2|c| > b
    3. 0 < c < √2b
    4. no real value of a
    Choice A
    |c| > √2|b|

  25. IPMAT 2019 Question Paper - IPM Indore Quants,Functions

    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

    19

  26. IPMAT 2019 Question Paper - IPM Indore Quants,Functions

    The function f(x) = \\frac{x^{3} - 5x^{2} - 8x}{3}\\) is

    1. positive and monotonically increasing for x \\in (-\infty, \frac{5-\sqrt{57}}{2}\\)) and x \\in (\frac{5+\sqrt{57}}{2}, +\infty\\))
    2. negative and monotonically decreasing for x \\in (-\infty, \frac{5-\sqrt{57}}{2}\\) and x \\in (\frac{5+\sqrt{57}}{2},+\infty\\))
    3. negative and monotonically increasing for x \\in (-\infty, \frac{5-\sqrt{57}}{2}\\)) and positive and monotonically increasing for x \\in (\frac{5+\sqrt{57}}{2},+\infty\\))
    4. positive and monotonically increasing for x \\in (-\infty, \frac{5-\sqrt{57}}{2}\\)) and negative and monotonically decreasing for x \\in (\frac{5+\sqrt{57}}{2},+\infty\\))
    Choice C
    negative and monotonically increasing for x \\in (-\infty, \frac{5-\sqrt{57}}{2}\\)) and positive and monotonically increasing for x \\in (\frac{5+\sqrt{57}}{2},+\infty\\))

  27. IPMAT 2019 Question Paper - IPM Indore Quants,Functions

    For a > b > c > 0, the minimum value of the function f(x) = |x - a| + |x - b| + |x - c| is

    1. 2a - b - c
    2. a + b - 2c
    3. a + b + c
    4. a - c
    Choice D
    a - c

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.


  1. CAT 2017 Question Paper Slot 1 - Functions

    If f1(x) = x2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is: (TITA)

    24

  2. CAT 2017 Question Paper Slot 1 - Functions

    If f(x) = \\frac{5x + 2}{3x - 5}) and g(x) = x2 – 2x – 1, then the value of g(f(f(3))) is:

    1. 2
    2. \\frac{1}{3})
    3. 6
    4. \\frac{2}{3})
    Choice A
    2

  3. CAT 2017 Question Paper Slot 2 - Functions

    Let f(x) = x2 and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

    1. 16
    2. 18
    3. 36
    4. 40
    Choice C
    36

  4. CAT 2017 Question Paper Slot 2 - Functions

    If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is [TITA]

    1

  5. CAT 2017 Question Paper Slot 2 - Functions

    Let f(x) = 2x – 5 and g(x) = 7 – 2x. Then |f(x) + g(x)| = |f(x)| + |g(x)| if and only if

    1. \\frac{5}{2}) < x < \\frac{7}{2})
    2. x ≤ \\frac{5}{2}) or x ≥ \\frac{7}{2})
    3. x < \\frac{5}{2}) or x ≥ \\frac{7}{2})
    4. \\frac{5}{2}) ≤ x ≤ \\frac{7}{2})
    Choice D
    \\frac{5}{2}) ≤ x ≤ \\frac{7}{2})

  6. CAT 2018 Question Paper Slot 1 - Functions

    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]

    54

  7. CAT 2018 Question Paper Slot 1 - Functions

    Let f(x)=min{2x2, 52 - 5x}, where x is any positive real number.Then the maximum possible value of f(x) is [TITA]

    32

  8. CAT 2018 Question Paper Slot 2 - Functions

    Let f(x)=max{5x, 52 - 2x2}, where x is any positive real number.Then the minimum possible value of f(x) is (TITA)

    20

  9. CAT 2019 Question Paper Slot 1 - Functions

    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]

    10

  10. CAT 2019 Question Paper Slot 1 - Functions

    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 (2n - 1) then a is equal to. [TITA]

    3

  11. CAT 2019 Question Paper Slot 2 - Functions

    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]

    12

CAT Online Coaching | CAT Algebra Videos On YouTube


Other useful sources for Algebra Questions | Functions Sample Questions



CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com