Section 1.5- Inverses

Finding the inverse of functions are based on composition

ex. Find inverse of F(x)

F(x)=2x-3

F^-1(x)= x+3/2

(FoF^-1)(x)= F(F^-1(x))

= F (x+3/2)

= 2(x+3/2)

= x+3-3

= x

OR

(F^-1 o F)(x)= F^-1 (F(x))

= F^-1 (2x-3)

= 2x-3+3/2

= 2x/2

= x

*You should get x regardless of which way you solve it

- two functions, f and g, are inverses of each other if and only if....

(F o G) (x)= (G o F)(x)= x

*graphs are reflections by Y=X

One-to-one function- passes horizontal line test and has inverse that is a function

-A function is a one-to-one function if and only if F(a)=F(b)----> a=b