Question
(a) write formulas for $f \circ g$ and $g \circ f$ and find the (b) domain and (c) range of each.$$f(x)=x^{2}, g(x)=1-\sqrt{x}$$
Step 1
For $f \circ g$, we substitute $g(x)$ into $f(x)$, so we get $f(g(x)) = (1-\sqrt{x})^2 = 1 - 2\sqrt{x} + x$. For $g \circ f$, we substitute $f(x)$ into $g(x)$, so we get $g(f(x)) = 1 - \sqrt{x^2} = 1 - |x|$. Show more…
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