Composite Function Value Calculation

CAT 2017 Slot 2 · Quantitative Ability · Medium · Functions

This is a medium Quantitative Ability question from the CAT 2017 Slot 2 paper. It tests Functions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 2017 Slot 2 questions More Functions questions All CAT QA

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

Answer

Explanation

At $x = 1$ : $g(1) = 2^1 = 2$ $f(1) = 1^2 = 1$

Now, evaluate $f(g(1))$ : $f(2) = 2^2 = 4$

Evaluate $g(f(1))$ : $g(1) = 2^1 = 2$

Sum $= f(g(1)) + g(f(1)) = 4 + 2 = 6$ .

Finally, $f(6) = 6^2 = 36$ .

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace

Composite Function Value Calculation

Explanation

Related Functions questions

Practise this under exam conditions