Question

A(x) = 5x^1/5-2Find the inverse

Answer 1

For this type of question, first, we set the following equation:

$y=5x^{\frac{1}{5}}-2$

Then, we exchange y and x:

$x=5y^{\frac{1}{5}}-2$

Now, we solve the above equation for y:

$\begin{gathered} x+2=5y^{\frac{1}{5}} \\ y^{\frac{1}{5}}=\frac{x+2}{5} \\ y=(\frac{x+2}{5})^5 \end{gathered}$

Answer:

$A^{-1}(x)=(\frac{x+2}{5})^5$