Question

If $f:R\to R,g:R\to R$ are define 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

Answer: (B)

$\frac{111}{25}$

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

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

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

$\left(go{f}^{-1}\right)\left(3\right)=g\left(f^{-1}\left(3\right)\right)=g\left(\frac{6}{5}\right)=\frac{111}{25}$