Question

If $f:R\to R,f\left(x\right)=x^3+3$, and $g:R\to R,g\left(x\right)=2x+1$, then $f^{-1}o{g}^{-1}\left(23\right)$ equals

• A. $2$
• B. $3$
• C. $(14{)}^{1/3}$
• D. $(15{)}^{1/3}$

Answer 1

Answer: (A)

$2$

We have $f\left(x\right)=x^3+3$ & $g\left(x\right)=2x+1$

$\therefore f^{-1}\left(x\right)=(x-3{)}^{1/3}$ & $g^{-1}\left(x\right)=\frac{(x-1)}{2}$

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

$\therefore f^{-1}o{g}^{-1}\left(23\right)=f^{-1}\left[g^{-1}\right(23\left)\right]=f^{-1}\left(11\right)$

$=(11-3{)}^{1/3}=(8{)}^{1/3}=2$