# CAT 2017 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Functions Questions | Question 23

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Question 23 : 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

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##### Method of solving this CAT Question from Functions

Given that f(x) = x2 and g(x) = 2x.
We have to find the value of f(f(g(x)) + g(f(x))) at x = 1,
⟹ g(1) = 21 = 2 ; f(1) = 12 = 1
First, let us find the value of f(g(x)) + g(f(x)) at x = 1,
⟹ f(g(1)) + g(f(1)) = f(2) + g(1)
⟹ 22 + 2
⟹ 6
Therefore, f(g(1)) + g(f(1)) = 6.
The value of f(f(g(1)) + g(f(1))) = f(6)
⟹ f(6) = x2 = 62 = 36

The question 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"

##### Hence, the answer is 36

Choice C is the correct answer

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