Question

$f:R\to R,g:R\to R$ defined as $f\left(x\right)=3x-4,g\left(x\right)=2+3x$ then $\left(g^{-1}o{f}^{-1}\right)\left(5\right)=$

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{5}$

Answer 1

Answer: (C)

$\frac{1}{3}$

$f\left(x\right)=y=3x-4\Rightarrow x=\frac{y+4}{3}=f^{-1}\left(y\right)$

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

$\therefore g^{-1}o{f}^{-1}\left(5\right)=g^{-1}\left(f^{-1}\right(5\left)\right)$

$g^{-1}o{f}^{-1}\left(5\right)=g^{-1}\left(f^{-1}\right(y\left)\right)=\frac{\frac{y+4}{3}-2}{3}=\frac{y-2}{9}$

$\therefore g^{-1}o{f}^{-1}\left(5\right)=g^{-1}\left(f^{-1}\right(5\left)\right)=\frac{5-2}{9}=\frac{1}{3}$