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 $\left(go{f}^{-1}\right)\left(3\right)$=

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

Answer 1

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

$f:R\to R$

$g:R⟶R$

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

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

$\left(go{f}^{-1}\right)\left(3\right)$

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

Let $f\left(x\right)=y$ $\Rightarrow x=f^{-1}\left(y\right)$

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

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

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

$f^{-1}\left(x\right)=\frac{x+3}{5}$ and $g\left(x\right)=x^2+3$

$\left(go{f}^{-1}\right)\left(3\right)=g\left[f^{-1}\left(3\right)\right]=g\left(\frac{3+3}{5}\right)=g\left(\frac{6}{5}\right)$

$=[{\left(\frac{6}{5}\right)}^2+3]=\frac{36}{25}+3=\frac{111}{25}$

Hence, $\frac{111}{25}$ is the correct answer.