Question

What is the inverse of `f(x)=-5x+2`?

Answer 1

Consider `y=-5x+2`

Our goal is to find the anti-image of x

`y-2=-5x`

`x=(-y+2)/5`

Then the function inverse is `y=(-x+2)/5=f^(-1)(x)`

We can test the solution solving `f o f^(-1)`

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

So `fof^(-1)=identity` and `f^(-1)` is the inverse of `f`