Graphing inverse functions Find the inverse function (on the given interval, if specificd) and graph both fand $f^{-1}$ on the same set of axes. Check your work by looking for the required symmetry in the graphs. $$f(x)=x^{4}+4, \text { for } x \geq 0$$
Added by Scott W.
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To do this, we need to switch the roles of $x$ and $y$ and solve for $y$: $$x = y^4 + 4$$ $$x - 4 = y^4$$ $$\sqrt[4]{x-4} = y$$ So, the inverse function of $f(x)$ is: $$f^{-1}(x) = \sqrt[4]{x-4}, \text{ for } x \geq 4$$ Show more…
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