Wait something is wrong my example:

you said that I'm right but according to your explanation, I am wrong also in my example.

"Look":

I got f-1(x) = x - 3 = y

and you said

**x = y - 3** --> f-1(x) = x - 3 but if you rearrange what you wrote in bold, you'd get y = x+3 and not y = x-3.

It doesn't matter how you call your variables: if then the inverse function is because
I did switch in my example because:

f(x) = y and f-1(x) = y (of inverse function)

y = x + 3

x = y + 3

y = x - 3

f-1(x) = x - 3

Something is either wrong or really confusing here so I was hoping I could get this cleared before proceeding to the actual problem.