Question

If $f:R\to R,g:R\to R$ are defined by $f\left(x\right)=5x-3,g\left(x\right)=x^2+3,$ then $\left(go{f}^{-1}\right)\left(3\right)$ is equal to

• A. $\frac{25}{3}$
• B. $\frac{111}{25}$
• C. $\frac{9}{25}$
• D. $\frac{25}{111}$

Answer 1

The correct option is B $\frac{111}{25}$

$f\left(x\right)=5x-3$

Let $y=5x-3$

$\Rightarrow x=\frac{y+3}{5}$

$\therefore f^{-1}\left(x\right)=\frac{x+3}{5}$

$f^{-1}\left(3\right)=\frac{6}{5}$

$g\left(x\right)=x^2+3$

${\mathrm{gof}}^{-1}\left(3\right)=g\left(f^{-1}\right(3\left)\right)=g\left(\frac{6}{5}\right)=\frac{36}{25}+3$

${\mathrm{gof}}^{-1}\left(3\right)=\frac{111}{25}$