Question

Benjamin Limberg Question 14 - 1 Point Mar 08, 2:24:51 PM For the function f(x)=((x-9)^((1)/(3)))/(5), find f^(-1)(x).

Answer 1

To find the inverse function of f(x) = (x - 9)^(1/3) / 5, transpose x and y, then solve for y step-by-step to get the inverse function: f^-1(x) = (5x)^3 + 9.

Step-by-step explanation:

To find the inverse function f-1(x) of the function f(x) = (x - 9)1/3 / 5, we need to swap the roles of x and y and then solve for y.

1. Start with the original function, y = (x - 9)1/3 / 5.
2. Replace y with x to get x = (y - 9)1/3 / 5.
3. Multiply both sides by 5 to eliminate the fraction: 5x = (y - 9)1/3.
4. Raise both sides to the power of 3 to get rid of the cube root: (5x)3 = y - 9.
5. Add 9 to both sides to isolate y: y = (5x)3 + 9.
6. Thus, the inverse function is f-1(x) = (5x)3 + 9.