Question

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

• A. $\frac{1}{10x-7}$
• B. $\frac{1}{10x+7}$
• C. $\frac{x+7}{10}$
• D. $\frac{x-7}{10}$

Answer 1

The correct option is C $\frac{x+7}{10}$

Here, $f\left(x\right)=10x-7$
which is clearly bijective as linear in $x$.
Let $y=f\left(x\right)$. So,
$y=10x-7$
$\Rightarrow y+7=10x$
$\Rightarrow \frac{y+7}{10}=x=g\left(y\right)$ as $\left(f\right(x)=y\Rightarrow x=f^{-1}(y\left)\right)$
$\Rightarrow g\left(x\right)=\frac{x+7}{10}$.