Question

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

Answer 1

Let $f^{-1}\left(x\right)=y$ ---- ( 1 )

$\Rightarrow$ $f\left(y\right)=x$

It is given that, $f\left(x\right)=10x-7$, then $f\left(y\right)=10y-7$.

$\Rightarrow$ $10y-7=x$

$\Rightarrow$ $10y=x+7$

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

From ( 1 ),

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