Question

If $f:R\to R$ defined by $f\left(x\right)=\frac{3x-1}{7}$ be an invertible function then write $f^{-1}\left(x\right)$

Answer 1

Let $y=\frac{3x-1}{7}$
$\Rightarrow 7y+1=3x$
$\Rightarrow x=\frac{7y+1}{3}$
$\Rightarrow f\left(x\right)=y$
$\Rightarrow f^{-1}\left(y\right)=x$
$\Rightarrow f^{-1}\left(y\right)=\frac{7y+1}{3}$
Interchanging $x$ and $y$, we get
$\Rightarrow f^{-1}\left(x\right)=\frac{7x+1}{3}$