Question

1. - / 12.5 points 0/100 submissions use find the inverse function of f. f(t) = t³ + 7 f⁻¹(t) =

Explanation:

Step1: Replace \( f(t) \) with \( y \)

We start by writing the function as \( y = t^3 + 7 \).

Step2: Swap \( t \) and \( y \)

To find the inverse, we swap the roles of \( t \) and \( y \), so we get \( t = y^3 + 7 \).

Step3: Solve for \( y \)

First, subtract 7 from both sides: \( t - 7 = y^3 \). Then, take the cube root of both sides to solve for \( y \): \( y=\sqrt[3]{t - 7} \).

Step4: Replace \( y \) with \( f^{-1}(t) \)

We replace \( y \) with \( f^{-1}(t) \), so the inverse function is \( f^{-1}(t)=\sqrt[3]{t - 7} \).

Answer:

\(\sqrt[3]{t - 7}\)