Find the inverse function of $f$.
$$f ( x ) = x ^ { 5 } + 5$$
A) $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x } + 5$
B) $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } + 5$
C) $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x + 5 }$
D) $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x - 5 }$
E) $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } - 5$

Question

Quizplus · Accepted Answer

To find the inverse function, we need to solve for $x$ in terms of $y$. Starting with the given equation, we have:

$$y=x^5+5$$

Subtracting 5 from both sides:

$$y-5=x^5$$

Taking the fifth root of both sides:

$$\sqrt[5]{y-5}=x$$

So the inverse function is:

$$f^{-1}(x)=\sqrt[5]{x-5}$$

Therefore, the answer is D.

Find the Inverse Function Of fff f(x)=x5+5f ( x ) = x ^ { 5 } + 5f(x)=x5+5

Find the Inverse Function Of $f$ $f ( x ) = x ^ { 5 } + 5$