Question

What is the inverse of the following function? Leave your final answer in factored form.

f(x) = ^3√x+5
Note: When giving your answer, use y instead of answer was f ^ - 1 * (x) = x + 2 f-1(x). you would type y = x + 2

Answer 1

y = x³ - 5

Explanation:

The inverse of a function is obtained by swapping the roles of y and x, then solving for y.

Given the function f(x) = ^3√(x+5), let's find its inverse:

1. Swap x and y: x = ^3√(y+5)

2. Solve for y:

To get rid of the cube root, we can cube both sides:

x³ = y + 5

Then, subtract 5 from both sides to isolate y:

y = x³ - 5

So, the inverse of the function f(x) = ^3√(x+5) is f^-1(x) = x³ - 5, or y = x³ - 5.