Question

Find the inverse of the cube root function $f$.
$f\left(x\right)={(x+1)}^{1/3}$

• A. $x^3+1$
• B. $x^3-1$
• C. $x-1$
• D. $x+1$

Answer 1

The correct option is B $x^3-1$

Let $y=f\left(x\right)={(x+1)}^{1/3}$ and now solve for $x$ to find the inverse of the given function.

$y={(x+1)}^{1/3}$, cubing both sides we get,

$y^3=x+1$

$x=y^3-1$

Therefore, the inverse of the function in terms of $x$ is $x^3-1$.