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If $$f \colon \mathbb{R} \rightarrow [0, \infty)$$ is defined by $$f(x) = x^2$$ and $$g \colon [0, \infty) \rightarrow \mathbb{R}$$ is defined by $$g(x) = \sqrt{x}$$ then does the function $$gof(x)$$ exist? If so what is the value of $$gof(-4)$$?
Correct Answer: 4
The range of $$f$$ is $$[0, \infty)$$, which is the domain of $$g$$, so $$gof$$ exists. It is $$gof(x) = \sqrt{x^2} = |x|$$. Hence $$gof(-4) = \sqrt{16} = 4$$.
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