Question

find a formula for the inverse of the following function, if possible.$p(x) = \sqrt5{x} - 1$answerhow to enter your answer (opens in new window) 2 pointskeypadkeyboard shortcutsselecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used.$p^{-1}(x) = \boxed{}$○ does not have an inverse function

Explanation:

Step1: Set $y = P(x)$

$y = \sqrt[5]{x} - 1$

Step2: Swap $x$ and $y$

$x = \sqrt[5]{y} - 1$

Step3: Isolate the radical term

$x + 1 = \sqrt[5]{y}$

Step4: Eliminate the 5th root

$(x + 1)^5 = y$

Answer:

$P^{-1}(x)=(x+1)^5$