Question 23

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

Solution

$$f[f(g(1)) + g(f(1))]$$
= $$f[f(2^1) + g(1^2)]$$
= $$f[f(2) + g(1)]$$
= $$f[2^2 + 2^1]$$
= $$f(6)$$
= $$6^2 = 36$$

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