CAT 2017 Question Paper | Quants Slot 2

CAT Questions

In order to prepare for the CAT Examcomprehensively, it is of utmost importance that you go through the CAT previous year paper to brace yourself for the googly that CAT Exam can throw at you. CAT 2017 Question Paper is your starting point! Don't wait, start right away with this question from functions taken from CAT Question Paper 2017 Slot 2. Do not look at the solution provided, solve the question yourself and kickstart your CAT Preparation Online .

Question 23 : Let f(x) = x² and g(x) = 2^x, 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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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Functions

Given that f(x) = x² and g(x) = 2^x.
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) = 2^x, 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