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How to Tell If Two Functions Are Inverses

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!