finding and verifying inverse

Question

Find the inverse of f(x)

F(x)=1/x-3

and then verify your result using (𝑓 ° 𝑓^−1)(𝑥) = 𝑥 and (𝑓^−1 ° 𝑓)(𝑥) = 𝑥.

Answer 1

I hope this helped!

Answer 2

y=1/(x-3) Change the y and the x

x=1/(y-3) Multiply both sides by (y-3)

(y-3)x=1/(y-3)(y-3) Simplify the right and and distribute the left

xy-3x=1 Add 3x to both sides

xy-3x+3x=1+3x Simplify

xy=1+3x Divide both sides by x

xy/x=(1+3x)/x Simplify

y=(1+3x)/x Sub in inverse notation

f^-1(x) = (1+3x)/x

This does check out, both equal x.