Question

find a formula for the inverse of the following function, if possible.\\( f(x) = sqrt5{x} - 3 \\)\\( f^{-1}(x) = \\)\\( \circ \\) does not have an inverse function\\( \text{answer how to enter your answer (opens in new window)} \\)\\( 2 \text{points} \\)\\( \text{selecting 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.} \\)\\( \text{keypad} \\)\\( \text{keyboard shortcuts} \\)

Explanation:

Step1: Set $y=F(x)$

$y = \sqrt[5]{x} - 3$

Step2: Swap $x$ and $y$

$x = \sqrt[5]{y} - 3$

Step3: Isolate the radical term

$x + 3 = \sqrt[5]{y}$

Step4: Eliminate the 5th root

$(x + 3)^5 = y$

Answer:

$F^{-1}(x)=(x+3)^5$