If f : R → R is defined by f(x) = 10 x − 7,
Question:

If $f: R \rightarrow R$ is defined by $f(x)=10 x-7$, then write $f^{-1}(x)$.

Solution:

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

$\Rightarrow f(y)=x$

$\Rightarrow 10 y-7=x$

$\Rightarrow 10 y=x+7$

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

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