Answer: [tex]f^{-1}(x)=-x+3[/tex]
Step-by-step explanation:
To find the inverse of a function replace f(x) with x and replace the original x with y
[tex]f(x)=-x+3\\x=-y+3[/tex]
Now solve for y
[tex]x=-y+3[/tex]
First subtract 3 from both sides
[tex]x-3=-y+3-3\\x-3=-y[/tex]
Now divide both sides by -1 (this will make y positive)
[tex]\frac{x-3}{-1} =\frac{-y}{-1} \\-x+3=y[/tex]
Now replace y with the inverse of f(x), [tex]f^{-1}(x)[/tex]
