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Let's do another easy one we already know:

f( x ) = x^2 ... for x is greater than or equal to 0
and
g( x ) = square root( x )

1 )  ( f o g )( x ) = f( g( x ) )


1 )  f( blob ) = ( blob )^2

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

3 )  f( square root( x ) ) = ( square root( x ) )^2 = x

 


2 )  ( g o f )( x ) = g( f( x ) )


1 )  g( blob ) = square root( blob )

2 )  g( f( x ) ) = square root( f( x ) )

3 )  g( x^2 ) = square root( x^2 ) = x

 

Uh...  Did you notice something weird too?

We got x's again.

That's no coincidence, Baby!