Problem

For the function $f(x)=\sqrt[3]{x}+4$, find $f^{-1}(x)$.

Answer

Expert–verified
Hide Steps
Answer

Final Answer: \(\boxed{f^{-1}(x) = (x - 4)^3}\)

Steps

Step 1 ：Given function: \(y = \sqrt[3]{x} + 4\)

Step 2 ：Swap x and y: \(x = \sqrt[3]{y} + 4\)

Step 3 ：Solve for y: \(y = (x - 4)^3\)

Step 4 ：Final Answer: \(\boxed{f^{-1}(x) = (x - 4)^3}\)

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More