Composite Functions — CAT Previous-Year Questions
19 previous-year questions on Composite Functions from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Composite Functions · CAT PYQs
Suppose for all integers x, there are two functions f and g such that f(x) + f(x - 1) - 1 = 0 and g(x) = x2. If f(x2 - x) = 5, then the value of the sum f(g(5)) + g(f(5)) is
Let r be a real number and f(x) = Then, the equation f(x) = f(f(x)) holds for all real values of x where
If f(x) = x2 – 7x and g(x) = x + 3, then the minimum value of f(g(x)) – 3x is
Let f(x) = x² + ax + b and g(x) = f(x + 1) – f(x – 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is
If f(x) = (5x+2)/(3x-5) and g(x) = x2 – 2x – 1, then the value of g(f(f(3))) is:
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
Answer the following question based on the information given below.
f1(x) = x 0 ≤ x ≤ 1
= 1 x ≥ 1
= 0 otherwise
f2(x) = f1(–x) for all x
f3(x) = –f2(x) for all x
f4(x) = f3(–x) for all x
How many of the following products are necessarily zero for every x
f1(x)f2(x), f2(x)f3(x), f2(x)f4(x)?
Answer the following question based on the information given below.
f1(x) = x 0 ≤ x ≤ 1
= 1 x ≥ 1
= 0 otherwise
f2(x) = f1(–x) for all x
f3(x) = –f2(x) for all x
f4(x) = f3(–x) for all x
Which of the following is necessarily true?
If then f(x) + f(y) =
Answer the following question based on the information given below.
For a real number x, let
f(x) = 1/(1 + x), if x is non-negative
= 1+ x, if x is negative
f n(x) = f(f n – 1(x)), n = 2, 3, ....
What is the value of the product, f(2)f2(2)f3(2)f4(2)f5(2)?
Answer the following question based on the information given below.
For a real number x, let
f(x) = 1/(1 + x), if x is non-negative
= 1+ x, if x is negative
f n(x) = f(f n – 1(x)), n = 2, 3, ....
r is an integer > 2. Then, what is the value of f r – 1(–r) + f r(–r)+ f r + 1 (–r)?
Directions: Answer the questions based on the following information.
Let x and y be real numbers and let
f (x,y) = |x + y| , F(f (x,y)) = −f (x,y)
and G(f (x, y)) = −F(f (x, y))
What is the value of f(G(f(1, 0)), f(F(f(1, 2)), G(f(1, 2))))?
Directions: Answer the questions based on the following information.
Let x and y be real numbers and let
f (x,y) = |x + y| , F(f (x,y)) = −f (x,y)
and G(f (x, y)) = −F(f (x, y))
Which of the following expressions yields x2 as its result?
Direction: Answer the questions based on the following information.
A, S, M and D are functions of x and y, and they are defined as follows.
A(x, y) = x + y
S(x, y) = x – y
M(x, y) = xy
D(x, y) = , y ≠ 0
What is the value of M(M(A(M(x, y), S(y, x)), x), A(y, x)) for x = 2, y = 3?
Direction: Answer the questions based on the following information.
A, S, M and D are functions of x and y, and they are defined as follows.
A(x, y) = x + y
S(x, y) = x – y
M(x, y) = xy
D(x, y) = , y ≠ 0
What is the value of S[M(D(A(a, b), 2), D(A(a, b), 2)), M(D(S(a, b), 2), D(S(a, b), 2))]?
Answer the next 4 questions based on the information given below:
If f (x) = 2x + 3 and g(x) = then
fog(x) is equal to
Answer the next 4 questions based on the information given below:
If f (x) = 2x + 3 and g(x) = then
For what value of x; f (x) = g(x −3)?
Answer the next 4 questions based on the information given below:
If f (x) = 2x + 3 and g(x) = then
What is the value of (gofofogogof)(x) × (fogofog)(x)?
Answer the next 4 questions based on the information given below:
If f (x) = 2x + 3 and g(x) = then
What is the value of fo(fog)o(gof)(x)?