Question

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

Answer 1

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