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How to Tell If Two Functions Are Inverses

 
If ( f o g )( x ) = x or ( g o f )( x ) = x ,

then f(x) and g(x) are inverse functions.

So, you really only need to check one of them!

Check it out:

Are these inverse functions?

f( x ) = 2x - 5 and g( x ) = ( 1 / 2 )x + ( 5 / 2 )


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


       1 ) f( blob ) = 2( blob ) - 5

       2 ) f( g( x ) ) = 2( g( x ) ) - 5

       3 ) f( ( 1 / 2 )x + ( 5 / 2 ) ) = 2( ( 1 / 2 )x + ( 5 / 2 ) ) - 5 = x + 5 - 5 = x ... Yep!

You can double-check it by crunching ( g o f )( x )  .

 

YOUR TURN:

Are these inverse functions?

f( x ) = x^2 - 3 and g( x ) = square root( x + 3 )

Are these inverse functions?

f( x ) = 2x - 5 and g( x ) = ( 1 / 2 )x + 5