Question

Needing some help with this one im trying to find the inverse of the one to one function

Answer 1

Here are the steps in getting the inverse of the given function:

1. Replace f(x) with y.

`y=2x-7`

2. Switch x and y.

`x=2y-7`

3. Isolate y.

Add 7 on both sides of the equation.

`\begin{gathered} x+7=2y-7+7 \\ x+7=2y \end{gathered}`

Divide both sides of the equation by 2 to remove the 2 in 2y.

`(x+7)/(2)=(2y)/(2)`
`(x+7)/(2)=y`

4. Replace y with the symbol for the inverse of f(x).

`f^(-1)(x)=(x+7)/(2)`

The inverse of the given function is (x + 7)/2 as shown above.