text: # CAT Practice : Functions
  
  You are here: Home  CAT Questionbank   CAT Quant  Functions
  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
  
  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
  3. ### Compound functions
  
  Consider functions f(x) = x2 + 2x, g(x) = $\sqrt {{\rm{x + 1}}}$ and h(x) = g(f(x)). What are the domain and range of h(x)?
  
  • Compound functions
  • Medium
  4. ### 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
  Roughly 0.14
  • Greatest Integer Function
  • Hard
  5. ### 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. ### Domain and Range
  
  How many elements are present in the domain of 9–xCx+1?
  
  1. 5
  2. 6
  3. 4
  4. 7
  7. ### 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
  1/9
  • Unconventional Question
  • Medium
  8. ### 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
  9. ### 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
  10. ### 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
  14/3
  • Function of a function
  • Medium
  11. ### 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
  12. ### Function of a function
  
  The value of fogoh(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
  13. ### 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)
  14. ### 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)
  15. ### 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
  • Greatest Integer Function
  • Medium
  16. ### 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
  • Greatest Integer Function
  • Medium
  17. ### 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
  • Greatest Integer Function
  • Medium
  18. ### 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))))))))
  19. ### 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
  20. ### 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
  21. ### 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
  22. ### Value of f(x)
  
  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
  23. ## Our Online Course, Now on Google Playstore!
  
  ### Fully Functional Course on Mobile
  
  All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.
  
  ### Cache Content for Offline Viewing
  
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explanation: This document contains a series of math questions and, in some cases, their corresponding answers. The questions are related to various topics in algebra, specifically functions, and are structured as multiple-choice questions. Each question is followed by a set of answer choices, and in some cases, the correct answer is provided.
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  Output rules:
  
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distilabel_metadata.content: # CAT Practice : Functions
  
  You are here: Home  CAT Questionbank   CAT Quant  Functions
  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
  
  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
  3. ### Compound functions
  
  Consider functions f(x) = x2 + 2x, g(x) = $\sqrt {{\rm{x + 1}}}$ and h(x) = g(f(x)). What are the domain and range of h(x)?
  
  • Compound functions
  • Medium
  4. ### 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
  Roughly 0.14
  • Greatest Integer Function
  • Hard
  5. ### 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. ### Domain and Range
  
  How many elements are present in the domain of 9–xCx+1?
  
  1. 5
  2. 6
  3. 4
  4. 7
  7. ### 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
  1/9
  • Unconventional Question
  • Medium
  8. ### 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
  9. ### 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
  10. ### 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
  14/3
  • Function of a function
  • Medium
  11. ### 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
  12. ### Function of a function
  
  The value of fogoh(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
  13. ### 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)
  14. ### 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)
  15. ### 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
  • Greatest Integer Function
  • Medium
  16. ### 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
  • Greatest Integer Function
  • Medium
  17. ### 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
  • Greatest Integer Function
  • Medium
  18. ### 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))))))))
  19. ### 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
  20. ### 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
  21. ### 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
  22. ### Value of f(x)
  
  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
  23. ## Our Online Course, Now on Google Playstore!
  
  ### Fully Functional Course on Mobile
  
  All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.
  
  ### Cache Content for Offline Viewing
  
  Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: This document contains a series of math questions and, in some cases, their corresponding answers. The questions are related to various topics in algebra, specifically functions, and are structured as multiple-choice questions. Each question is followed by a set of answer choices, and in some cases, the correct answer is provided.
  
  Label: multiple-question-and-answer