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Composition of Functions

Here's another one -- let's do the guy we started before:

Givenf( x ) = x^2 + 3andg( x ) = x - 2
 

Find

 

f( g( x ) )


      1 ) f( blob ) = ( blob )^2 + 3

      2) f( g( x ) ) = ( g( x ) )^2 + 3

      3 ) f( x - 2 ) = ( x - 2 )^2 + 3 = x^2 - 4x + 4 + 3 = x^2 - 4x + 7

YOUR TURN:

Givenf( x ) = 5x^2 + xandg( x ) = 3x - 1
Findf( g( x ) )

By the way, the official math notation for

f( g( x ) )is( f o g )( x )

This little guy here is NOT a multiplication dot.  I like to think of it as a little "o" for "of."  f OF g(x)

Why do we use this notation?  So that everyone thinks we're doing something really hard and that we're super smart.