Question

[find f ^{-1}(x) f(x)=\sqrt[3]{x-7}\]

Answer 1

Replace f(x) with y. Swap x and y. Then solve for y to get the inverse.


\[\Large f(x)=\sqrt[3]{x-7}\]


\[\Large y=\sqrt[3]{x-7}\]


\[\Large x=\sqrt[3]{y-7}\]


\[\Large x^3=y-7\]


\[\Large x^3+7=y\]


\[\Large y=x^3+7\]


\[\Large f^{-1}(x)=x^3+7\]

Answer 2

though I'm not quite sure how you solved it, thanks for your help, I will try these steps

Answer 3

you undo each operation

so you first undo the cube root by cubing both sides

then you undo the -7 by adding 7 to both sides