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

Question

asked May 26, 2023 204k views

1 Answer

Hitul Mistry · Answer 1 · 2023-06-01T14:42:01+0000

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)