Question

F(x)=(x 8)⁵ equation for f^⁻1 (x). Find inverse?

Answer 1

To find the inverse of the function f(x) = (x + 8)^5, switch x and y, solve for y, and rewrite the equation.

Step-by-step explanation:

To find the inverse of the function f(x) = (x + 8)^5, we need to switch the roles of x and y and solve for y. Let's start by rewriting the function with y as the variable:

y = (x + 8)^5

Next, we will interchange x and y:

x = (y + 8)^5

Now, we need to solve for y. To do this, we will take the fifth root of both sides:

y + 8 = x^(1/5)

Subtracting 8 from both sides:

y = x^(1/5) - 8

Therefore, the equation for f^⁻1(x) or the inverse of f(x) is:

f^⁻1(x) = x^(1/5) - 8