Question

Let $f$ : $R\to R$ be the function defined by $f(x)=x^3+5$. Then $f^{-1}(x)$ is

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

Answer 1

Answer: (B)

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