How many levels of composition do you see here?

h( x ) = sin^2 3x
 

Careful here!  Remember to write this as what it really means:

h( x ) = ( sin 3x )^2
 

I see three levels:

outside= (   )^2

middle

= sin(   )

inside

= 3x


Here's one more...  I do it below...  Try it before looking!

h( x ) = cos( Ln( 6x ) )^3

* read it out loud!

 

 


 

1 )outside= cos(   )
2 )

next in

= (   )^3
3 )

next in

= Ln(   )
4 )

inside

= 6x

 


TRY IT:

How many levels of composition do you see?  List them.

h( x ) = Ln( 4x - 1 )


h( x ) = tan^2 7x
 

h( x ) = square root( sin 3x )
 

h( x ) = sin^5 square root( 2x )