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

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36 — Easy Evaluate from the inside out at $x=1$: compute $f(g(1))$ and $g(f(1))$, add them, then apply the outer $f$ (squaring) to that sum. 1 Inner pieces at $x=1$. Here $f(x)=x^2$ and $g(x)=2^x$. $$\begin{aligned} &g(1) = 2^1 = 2 \;\Rightarrow\; f(g(1)) = f(2) = 2^2 = 4\ &f(1) = 1^2 = 1 \;\Rightarrow\; g(f(1)) = g(1) = 2^1 = 2 \end{aligned}$$ 2 Add the two pieces. Sum the results from step 1. $$\begin{aligned} &f(g(1)) + g(f(1)) = 4 + 2 = 6 \end{aligned}$$ 3 Apply the outer $f$. Square the sum. $$

CAT 2017 Slot 2 — QA Question 23

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