Question

Given $f\left(x\right)=\frac{x+2}{5}$ for $\text{gof}\left(x\right)=x-3$, find $g$.

Answer 1

Given, $f\left(x\right)=\frac{x+2}{5},\text{gof}\left(x\right)=x-3$

$g\left(\frac{x+2}{5}\right)=x-3$ ....(i)

Thus $\frac{x+2}{5}=z$

$\Rightarrow x=5z-2$

Substituting in (i), we get

$g\left(\frac{5z-2+2}{5}\right)=5z-2-3\Rightarrow g\left(z\right)=5(z-1)\Rightarrow g\left(x\right)=5(x-1)$