Question

Find the inverse function for f(x) = 675 + 2

Answer 1

Replace f(x) with y .

$y=6x^5\text{ + 2}$

$\begin{gathered} \text{make x the subject of the formular } \\ y-2=6x^5 \\ divide\text{ both sides by 6} \\ \frac{y-2}{6}=x^5 \\ \end{gathered}$$\begin{gathered} To\text{ make x stand alone } \\ \sqrt[5]{\frac{y-2}{6}}\text{ = x} \end{gathered}$

Swap x and y

$\sqrt[5]{\frac{x-2}{6}}\text{ = y}$

Therefore,

$f^{-1}(x)\text{ = }\sqrt[5]{\frac{x-2}{6}}$