Question

find a formula for the inverse of the following function, if possible. \\( p(x) = sqrt3{x} + 1 \\) \\( p^{-1}(x) = \\) \\( \circ \\) does not have an inverse function

Explanation:

Step1: Replace $P(x)$ with $y$

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

Step2: Swap $x$ and $y$

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

Step3: Isolate the cube root term

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

Step4: Cube both sides to solve for $y$

$(x - 1)^3 = y$

Step5: Replace $y$ with $P^{-1}(x)$

$P^{-1}(x) = (x - 1)^3$

Answer:

$P^{-1}(x) = (x - 1)^3$