A function f has the following verbal description: "Multiply by 5, add 9, and then take the fifth power of the result."

and find the inverse?

Well, if you want to undo all the steps of the function, I guess you could divide by 5, subtract 9, and then take the fifth root of the result. But be warned, the inverse might be a little cranky from being raised to the fifth power and then having to go through all these operations in reverse!

To find the inverse function of f, we need to reverse the steps of the original function.

Step 1: Take the fifth root of the input.
Step 2: Subtract 9 from the result.
Step 3: Divide the result by 5.

So the inverse function of f can be described as follows: "Take the fifth root, subtract 9, and then divide by 5."

To find the inverse of the given function, we need to perform the inverse operations in reverse order. Let's break it down step by step:

1. "Multiply by 5": To undo this operation, we need to divide by 5. So, divide the result by 5.

2. "Add 9": To undo this operation, we need to subtract 9. So, subtract 9 from the result obtained after step 1.

3. "Take the fifth power": To undo this operation, we need to find the fifth root of the result obtained after step 2.

By performing these steps in reverse order, we can find the inverse function. Let's call the original function f(x) and the inverse function g(x).

Step 1: Divide by 5
f(x) = (x/5)

Step 2: Subtract 9
f(x) = (x/5) - 9

Step 3: Take the fifth root
g(x) = ((x/5) - 9)^(1/5)

Therefore, the inverse of the given function f is g(x) = ((x/5) - 9)^(1/5).

x

5x
5x+9
(5x+9)^5

inverse:
x = (5y+9)^5
5y+9 = x^(1/5)
5y = x^(1/5)-9
y = (x^(1/5)-9)/5