Question

use algebra to find the inverse of the function ( f(x)=4 x^{7}+8 ) the inverse function is ( f^{-1}(x)= ) entry tip: to enter an answer like ( sqrtn{x} ), type ( operatorname{root}(n)(x) ). preview your answer before submitting! question help: video check answer

Explanation:

Step1: Replace \( f(x) \) with \( y \)

Let \( y = 4x^{7}+8 \)

Step2: Swap \( x \) and \( y \)

We get \( x = 4y^{7}+8 \)

Step3: Solve for \( y \)

First, subtract 8 from both sides: \( x - 8=4y^{7} \). Then divide both sides by 4: \( \frac{x - 8}{4}=y^{7} \). Finally, take the 7 - th root of both sides: \( y=\sqrt[7]{\frac{x - 8}{4}} \)

Answer:

\( f^{-1}(x)=\sqrt[7]{\frac{x - 8}{4}} \)