Question

If $f$:$R\to$ $R$ is defined as $f\left(x\right)=10x+7$. Find the function $g$:$R\to$ $R$, such that $gof=fog=IR$.

Answer 1

Here, $gof=fog=IR$

$\Rightarrow fog=IR$

Hence, $\Rightarrow fog\left(x\right)=I\left(x\right)$

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

Where $I\left(x\right)=x$ is an identity function

$\Rightarrow 10\left(g\right(x\left)\right)+7=x$

$\Rightarrow g\left(x\right)=\frac{x-7}{10}$

$\Rightarrow g:R\to R$ is a function defined as $g\left(x\right)=\frac{x-7}{10}.$