Question

f(x) = Vx + 7. Find the inverse of f(x).O A. f-'(x) = (x + 7)B. f-'(x) = 23 +7c. f-1(c) = 23 – 7O D. f-'(x) = (x – 7)SUBMIT

Answer 1

`f(x)=\sqrt[3]{x+7}`

1. Replace f(x) with y .

`y=\sqrt[3]{x+7}`

2. Replace every x with a y and replace every y with an x:

`x=\sqrt[3]{y+7}`

3. Solve for y:

`\begin{gathered} x^3=(\sqrt[3]{y+7})^3 \\ x^3=y+7 \\ y=x^3-7 \end{gathered}`

4. Replace y with f−1(x)

`f^(-1)(x)=x^3-7`