Question

The inverse of the function f(x)=-x+3

Answer 1

Answer:
`f^(-1)(x)=-x+3`

Explanation:

To find the inverse of a function replace f(x) with x and replace the original x with y

`f(x)=-x+3\\x=-y+3`

Now solve for y

`x=-y+3`

First subtract 3 from both sides

`x-3=-y+3-3\\x-3=-y`

Now divide both sides by -1 (this will make y positive)

`(x-3)/(-1) =(-y)/(-1) \\-x+3=y`

Now replace y with the inverse of f(x),
`f^(-1)(x)`