Question:
If $f: R \rightarrow R$ defined by $f(x)=3 x-4$ is invertible, then write $f^{-1}(x)$.
Solution:
Let $f^{-1}(x)=y$ $\ldots(1)$
$\Rightarrow f(y)=x$
$\Rightarrow 3 y-4=x$
$\Rightarrow 3 y=x+4$
$\Rightarrow y=\frac{x+4}{3}$
$\Rightarrow f^{-1}(x)=\frac{x+4}{3} \quad[$ from (1) $]$