Question

Question 5 OT IUIf f(x) = 9x - 8, which of the following is the inverse of f(x)?O A. (*) - X=8B. f-1(x)X+98O c. f'(x) = X 48O D. F-1(x) = X-98SUBMIT

Answer 1

To determine the inverse of a function we can follow these steps:

1. Replace f(x) by "y".

2. Switch the places of "y" and "x" on the expression.

3. Isolate the "y" variable on the left side.

4. Replace "y" by f^-1(x).

Let's apply these steps to the given expression:

`\begin{gathered} f(x)=9x-8 \\ y=9x-8 \end{gathered}`

Now we can apply the second step:

`x=9y-8`

We can now follow the third step:

`\begin{gathered} 9y=x+8 \\ y=(x+8)/(9) \end{gathered}`

Now the final step:

`f^(-1)(x)=(x+8)/(9)`

The expression for the inverse is (x+8)/9.