Answer:
[tex] {f}^{ - 1} (x) = 3 {x}^{2} - 3[/tex]
Step-by-step explanation:
We want to find the inverse of
[tex] y = \sqrt[3]{ \frac{x}{3} + 1} [/tex]
We interchange x and y to get:
[tex]x= \sqrt[3]{ \frac{y}{3} + 1} [/tex]
We solve for y;
[tex] {x}^{2} = \frac{y}{3} + 1[/tex]
Multiply through by 3
[tex]3 {x}^{2} = y + 3[/tex]
Subtract 1 from both sides:
[tex]y = 3 {x}^{2} - 3[/tex]
Therefore the inverse is
[tex] {f}^{ - 1} (x) = 3 {x}^{2} - 3[/tex]
