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

A) 16

B) 18

C) 36

D) 40

Option (C)

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,

f(g(x)) = 2^(2x)

g(f(x)) = 2^((x)^2)

f(f(g(x)) + g(f(x)) = (2^(2x) + 2^(x^2))^2

at x = 1, we get 36

Option (C)

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