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Composition of Functions

Check this out:

Given f( x ) = 6x + 1 and g( x ) = 2x^2 + 5
 

Find

  

f( g( x ) ) :
 
1 )
Find
f( blob ) :
f( blob ) = 6( blob ) + 1
  2 ) Find f( g( x ) )

f( g( x ) ) = 6( g( x ) ) + 1
 

  3 ) Replace the g( x ) with 2x^2 + 5
since g( x ) = 2x^2 + 5

f( 2x^2 + 5 ) = 6( 2x^2 + 5 ) + 1
Yeah, this is the answer, but we
always clean it up to be polite.

f( 2x^2 + 5 ) = 12x^2 + 30 + 1 = 12x^2 + 31