Question

If $f:R\to R,f\left(x\right)=4x^3+3$, then $f^{-1}\left(x\right)$ equals-

• A. ${\left(\frac{x-3}{4}\right)}^{1/3}$
• B. $\left(\frac{x^{1/3}-3}{4}\right)$
• C. $\frac{1}{4}(x-3{)}^{1/3}$
• D. $Noneofthese$

Answer 1

The correct option is A ${\left(\frac{x-3}{4}\right)}^{1/3}$

$f\left(x\right)=4x^3+3=y$

$4x^3=(y-3)$

$x^3=\frac{y-3}{4}$

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

$f^{-1}\left(x\right)={\left(\frac{x-3}{4}\right)}^{1/3}$.