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 of a function, we switch the roles of x and y and then solve for y. So, let's write the equation as:

$$y = x^5 + 5$$

Now, let's switch the roles of x and y:

$$x = y^5 + 5$$

Solving for y:

$$x - 5 = y^5$$

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

Thus, the inverse function of $f(x) = x^5 + 5$ 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 $f$ $f ( x ) = x ^ { 5 } + 5$