inverses

today im teaching you how to find inverses. there is a couple of rules though. the first rule is that to have an inverse that is a fumction it has to cross the horizontal line test. to find the inverses all you are going to do is switch the x's and the y's and solve for y. to prove something is an inverse do (f o *inverse of* f) (x) and (*inverse of* f o f) and both should equal x. so below i will provide an example.


EX:
state whether the function f has an invers. if f^-1 exists then find a rule to prove it.

f(x)= 3x - 5
first switch x and y
x=3y - 5
solve for y
y= x + 5 / 3
now prove it
(f o f^-1)= f(x)= 3(x+5 / 3) -5
3's cancel leaving you with x+5 - 5 which = x
(f^-1 o f)= f^-1(x)= (3x - 5) +5 / 3
3's cancel 5's cancel leaving you with x
these are inverses