CAT Practice : Functions

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The following topics are covered in the CAT quant section from Algebra: Functions. Detailed explanatory answers, solution videos and slide decks are also provided.
  1. 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
  2. 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
  3. 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
  4. 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)?

    • Correct AnswerDomain: ( -∞, +∞), Range -[0, ∞] Correct answer
    • Explanatory Answer
    • Compound functions
    • Medium
  5. Greatest Integer Function

    [x] = greatest integer less than or equal to x. If x lies between 3 and 5, what is the probability that [x2] = [x]2?

    1. Roughly 0.64
    2. Roughly 0.5
    3. Roughly 0.14
    4. Roughly 0.36
    • Correct AnswerChoice (C).
      Roughly 0.14
      Correct answer
    • Explanatory Answer
    • Greatest Integer Function
    • Hard
  6. 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
  7. Domain and Range

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

    1. 5
    2. 6
    3. 4
    4. 7
  8. 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
    • Correct AnswerChoice (B).
      1/9
      Correct answer
    • Explanatory Answer
    • Unconventional Question
    • Medium
  9. 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
  10. 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
  11. 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
    • Correct AnswerChoice (B).
      14/3
      Correct answer
    • Explanatory Answer
    • Function of a function
    • Medium
  12. Identical Functions

    Which of the following functions are identical? f(x) =
    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
  13. Function of a function

    The value of fogoh(9) could be, if
    f(x) =
    g(x) =
    h(x) = √x

    1. 3
    2. -5
    3. None of these
  14. Function of a function

    For this question, assume the following operators: A*B = A2 - B2
    A-B =
    A+B = A * B
    = A+B
    Which of the following expression would yield the result as x subtracted by y?

    1. (x*y)-(x+5)
    2. ()*(x-y)
    3. (x*y) - ()
    4. (x+y)*(x-y)
  15. Domain of Function

    Find the domain of: + √(x+1)

    1. (-∞,9)
    2. [-1,9)
    3. [-1,9) excluding 0
    4. (-1,9)
  16. Value of a Function

    If f(x).f(1/x) = -(f(x) + f(1/x)) and f(5) = 124. Find the value of f(1/8)

    1. 511
    2. Can’t be determined
  17. 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
    • Correct AnswerChoice (B).
      Correct answer
    • Explanatory Answer
    • Greatest Integer Function
    • Medium
  18. 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
    • Correct AnswerChoice (D).
      Correct answer
    • Explanatory Answer
    • Greatest Integer Function
    • Medium
  19. 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
    • Correct AnswerChoice (D).
      Correct answer
    • Explanatory Answer
    • Greatest Integer Function
    • Medium
  20. Composite Function

    If , 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))))))))
  21. Invertible Functions

    If . 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
  22. 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
  23. 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
  24. Value of f(x)

    If , 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
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