Check this out:

Givenf( x ) = 6x + 1andg( x ) = 2x^2 + 5
 

Find

 

f( g( x ) ) :

 
1 )

Find

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

f( g( x ) ) = 6( g( x ) ) + 1
 

 3 )Replace theg( x )with2x^2 + 5
sinceg( 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