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Composition of Functions

TRY IT:

Givenf( x ) = x^3 - 6x^2 - 5

f( blob ) =

f( g( x ) ) =

OK, so what if you had this:

f( x ) = 2x^2 + 5 ... f( blob ) + 2( blob )^2 + 5

Now, what if I told you to replace the word "blob" with "x+3" ?

blob = x + 3

f( blob ) = 2( blob )^2 + 5 ... f( x + 3 ) = 2( x + 3 )^2 + 5

This is the game!  First, we do the blob thing.  Then, we get with the notation and put the g(x) in...  Then, we replace that g(x) with whatever g(x) really is.  Don't worry.  It's easy!