Question 1041432
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*[Tex \LARGE f(x) = (x+4)^3]





*[Tex \LARGE y = (x+4)^3] Replace f(x) with y.





*[Tex \LARGE x = (y+4)^3] Swap x and y. Now solve for y.





*[Tex \LARGE \sqrt[3]{x^{ \ }} = \sqrt[3]{(y+4)^3}] Apply the cube root to both sides to undo the cubing. 





*[Tex \LARGE \sqrt[3]{x^{ \ }} = y+4] Notice how the cubing and cube root cancel on the right hand side.





*[Tex \LARGE y+4 = \sqrt[3]{x^{ \ }}]





*[Tex \LARGE y+4-4 = \sqrt[3]{x^{ \ }}-4] Subtract 4 from both sides.





*[Tex \LARGE y = -4+\sqrt[3]{x^{ \ }}]





*[Tex \LARGE f^{-1}(x) = -4+\sqrt[3]{x^{ \ }}] Now that y is fully isolated, replace it with the inverse function notation *[Tex \Large f^{-1}(x)]



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The inverse function is *[Tex \LARGE f^{-1}(x) = -4+\sqrt[3]{x^{ \ }}]



where *[Tex \LARGE \sqrt[3]{x^{ \ }}] is the cube root of x.
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