Question

$f:R\to R$ is a function defined by $f\left(x\right)=10x-7$. If $g=f^{-1}$, find $g\left(x\right)$.

Answer 1

Given, $f\left(x\right)=10x-7$

$\Rightarrow y=10x-7$

$\Rightarrow y+7=10x\Rightarrow x=\frac{y+7}{10}$

Interchanging $x$ and $y$

$\Rightarrow f^{-1}\left(x\right)=g=\frac{x+7}{10}$