Question

What is the inverse of cube root x/3 +1

Answer 1

Answer:

${f}^{ - 1} (x) = 3 {x}^{2} - 3$

Step-by-step explanation:

We want to find the inverse of

$y = \sqrt[3]{ \frac{x}{3} + 1}$

We interchange x and y to get:

$x= \sqrt[3]{ \frac{y}{3} + 1}$

We solve for y;

${x}^{2} = \frac{y}{3} + 1$

Multiply through by 3

$3 {x}^{2} = y + 3$

Subtract 1 from both sides:

$y = 3 {x}^{2} - 3$

Therefore the inverse is

${f}^{ - 1} (x) = 3 {x}^{2} - 3$