Question

If \(f : R \rightarrow R\) be a mapping defined by $f\left(x\right)=x^3+5$, then $f^{-1}x$ is equal to

• A. $(x+5{)}^{\frac{1}{3}}$
• B. $(x-5{)}^{\frac{1}{3}}$
• C. $(5-x{)}^{\frac{1}{3}}$
• D. $5-x$

Answer 1

The correct option is B $(x-5{)}^{\frac{1}{3}}$

$y=f\left(x\right)\Rightarrow y=x^3+5$
$\Rightarrow x=(y-5{)}^{\frac{1}{3}}$
$\therefore f^{-1}\left(x\right)=(x-5{)}^{\frac{1}{3}},xϵR$