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F (x) = ^3 square root x- 15. Find the inverse of f(x).

F (x) = ^3 square root x- 15. Find the inverse of f(x).-example-1
User Mystical
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1 Answer

4 votes

Given the function


f(x)=\sqrt[3]{x-15}

we want to find the its inverse function


f^(-1)(x).

In order to do that, we will replace f(x) with y. This is done to make the rest of the process easier. So, we have


y=\sqrt[3]{x-15}

Now, let's replace every x with a y and every y with an x,


x=\sqrt[3]{y-15}

and we must solve this equation for y. Then, by raising both sides to the third power, we get


x^3=y-15

and by adding 15 to both sides, we have


\begin{gathered} x^3+15=y \\ or\text{ equivalently,} \\ y=x^3+15 \end{gathered}

Finally, by replacing y with f^-1(x), we have


f^(-1)(x)=x^3+15

Therefore, the answer is option C.

User Shontauro
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