Question

if $f:R\to R,f\left(x\right)=2x+1$ and $g:R\to R,g\left(x\right)=x^3$, then $\left(gof{)}^{-1}\right(27)$ equals-

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is C $1$

According to question,

$f\left(x\right)=2x+1$ , $g\left(x\right)=x^3$

So, $y=g\left(f\right(x\left)\right)=(2x+1{)}^3$

$⟹\frac{y^{1/3}-1}{2}=x$

So, $y^{-1},i.e;(gof{)}^{-1}=\frac{x^{1/3}-1}{2}$

At, $x=27$,

$⟹\frac{(27{)}^{1/3}-1}{2}=\frac{3-1}{2}=1$