Question

f(x) = y2 – 15. Find the inverse of f(x).O A. f-1(x) = x3 + 15O B. f-1(x) = (x – 15)3O c. f-1(x) = (x + 15)3OD. f-'(x) = 2 - 15SUBMIT

Answer 1

$\text{Answer: f}^{-1\text{ }}(x)=x^3\text{ + 15}$

Answer: OPTION A

F(x) is given as

$\begin{gathered} F(x)\text{ = }\sqrt[3]{x\text{ - 15}} \\ \text{Let f(x) = y} \\ y\text{ = }\sqrt[3]{x\text{ - 15}} \\ \text{put y = x and x = y} \\ x\text{ = }\sqrt[3]{y\text{ - 15}} \\ x=(^{}y-15)^{\frac{1}{3}} \\ \text{Take the cube of both sides} \\ x^3\text{ = (}\sqrt[3]{y\text{ - 15}})^3 \\ x^3\text{ = y - 15} \\ y=x^3+15^{}^{} \\ f^{-1}(x)=x^3\text{ + 15} \end{gathered}$