Question

If $f:R\to R$ and $g:R\to R$ are defined by $f\left(x\right)=3x-4$ and $g\left(x\right)=2+3x$ then $(g^{-1}\circ f^{-1})\left(5\right)=$

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

Answer 1

Answer: (C)

$\frac{1}{3}$

$f\left(x\right)=3x-4$

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

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

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

$f^{-1}\left(5\right)=\frac{5+4}{3}=3$

$\left(g^{-1}o{f}^{-1}\right)\left(5\right)=g^{-1}\left[f^{-1}\right(5\left)\right]=g^{-1}\left(3\right)$

$=\frac{3-2}{3}=\frac{1}{3}$