Question

What is the inverse of the function `y = 2x + 5`?

Answer 1

If `f(x)=2x+5`
`f(x)^-1=(x-5)/2`

Explanation:

This method works, but I'm not sure how sound it is mathematically.

Let `f(x)=y`
so `y=2x+5`
then rearrange for `x`
so `x=(y-5)/2`
Now swap the subject for `f(x)^-1` and the `y` for `x`.
`f(x)^-1=(x-5)/2`

You can check the answer by substituting in a value for `x`, example `x=3`

`f(3)=6+5=11`
Then put the answer of that into the inverse equation, and you should receive the first number you put in.

`f(11)^-1=(11-5)/2=6/2=3`