Question

What is the inverse function of `f(x)=x-2` and how do you find `f^-1(0)`?

Answer 1

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

`f^-1(0)=2`

Explanation:

Let `y=f(x)` where `y` is the image of an object `x`.

Then the inverse function `f^-1(x)` is a function whose objects are `y` and whose images are `x`

This means that we are trying to find a function `f^-1` that takes inputs as `y` and the result is `x`

Here's how we proceed

`y=f(x)=x-2`

Now we make `x` the subject of the formula

`=>x=y+2`

Hence `f^-1=x=y+2`

This means that the inverse of `f(x)=x-2` is `color(blue)(f^-1(x)=x+2)`

`=>f^-1(0)=0+2=color(blue)2`