Notes from 2.4: Operations on Functions/ Composition of Functions

*Sorry these notes weren't up sooner, but I posted them before, and then they somehow didn't show up on the blog. Sorry guys*

1. Composition of a Function:
-(fog)(x) or “f circle g of x” aka f(g(x))
--f(x)=x2–5
--g(x)=3x-4
(fog)(x)=f(g(x))
=f(3x-4)
=(3x-4)2-5
=9x2-24x+16-5
(fog)(x)=9x2-24x+11
(gof)(x)=g(f(x))
=g(x2–5)
=3(x2–5)-4
=3x2-15-4
(gof)(x)=3x2-19
2. Inverses:
- use PEMDAS in reverse (SADMEP)
-inverses are always functions
-1/2 of inverse (quadratics) will show because the other half does not pass the vertical line test. (Seen in graphing on calculator)
--f(x)=2x-1
f-1(x)=
g(x)=(x-3)2
g-1(x)=
or:
g-1(x)= +3
3. Graphing Inverses:
-inverse will be a reflection of equation over the y=x line
-points switch from (x,y) to (y,x)

-graph vs. y=x

4. Algebra of Inverses:
--f(x)=
f-1(x) » y=
y=
x= (x switches places with y)
x2=y-3
y=x2+3 » f-1(x)= x2+3
D , D-1:
5. Algebra Cont. Checking for Inverses:
--f(x)=x3+1
--g(x)=
--(fog)(x)= (gof)(x)=x
f(g(x)): g(f(x)):
f( ) g(x3+1)
( 3+1 ) -1
x-1+1=x ) =x YES, they are inverses!
Homework (due Sept. 28) - 180:15-35 odd, 197: 1-15 odd, 33-41 odd, 71-80
Quiz (Sept. 26) – Quadratics, Solving with Calculator, Absolute Value, Inequalities, Application Problem