Question

suppose $f(x)=x^3 + 1$.
a) find the inverse function $f^{-1}(x)$.

Explanation:

Step1: Set $y = f(x)$

$y = x^3 + 1$

Step2: Swap $x$ and $y$

$x = y^3 + 1$

Step3: Isolate $y^3$

$y^3 = x - 1$

Step4: Solve for $y$

$y = \sqrt[3]{x - 1}$

Answer:

$f^{-1}(x) = \sqrt[3]{x - 1}$