Okay, here we have this:
We need to find the inverse of the following function:
[tex]f\mleft(x\mright)=\mleft(\frac{x^5}{7}\mright)^{\frac{1}{7}}-1[/tex]
First we will replace x with y:
[tex]x=\mleft(\frac{y^5}{7}\mright)^{\frac{1}{7}}-1[/tex]
Now, let's clear y:
[tex]\begin{gathered} \mleft(\frac{y^5}{7}\mright)^{\frac{1}{7}}-1=x \\ \mleft(\frac{y^5}{7}\mright)^{\frac{1}{7}}=x+1 \\ \frac{y^5}{7}=(x+1)^7 \\ y^5=7(x+1)^7 \\ y=\sqrt[5]{7(x+1)^7} \end{gathered}[/tex]
Finally we obtain that the correct answer is the second option.
