If $$f \colon \mathbb{R} \rightarrow \mathbb{R}$$ is a function defined by $$f(x) = 2|x| + 3$$ for every $$x$$ in $$\mathbb{R}$$ then draw the graph of $$f(f(x))$$.

Correct Answer: 0

Solution

PLACEHOLDER ANSWER - the answer is a graph, not a number. Since $$f(x) = 2|x| + 3 > 0$$, $$f(f(x)) = 2(2|x| + 3) + 3 = 4|x| + 9$$. Its graph is a V shape with vertex at $$(0, 9)$$, the line $$y = 4x + 9$$ for $$x \ge 0$$ and $$y = -4x + 9$$ for $$x < 0$$, symmetric about the $$y$$-axis.

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