Find the inverse of f (x) = - x + 3

Let g the inverse function of f.

The most important property of g and f being inverses of each other, is that

g (f (x)) = x, also f (g (x)) = x

so, what one function 'does' to x, the other 'undoes' it.

Thus, we have:

f (g (x)) = x and alos f (g (x)) = - g (x) + 3, from the rule

thus:

-g (x) + 3=x

-g (x) = x-3

g (x) = - x+3

check: f (g (x)) = f (-x+3) = - (-x+3) + 3=x-3+3=x

Answer: the inverse of f is g, such that g (x) = - x+3