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How to Tell if a Function Has an Inverse Function (One-to-One)

Check back...  Remember that I said we had to restrict it to x is greater than or equal to 0 ?

 Well, here's the graph of

f( x ) = x^( 2 ) for x is greater than or equal to 0 :
a graph of f( x ) = x^( 2 )  

Oh!

THIS guy IS one-to-one!

Get it now?

You saw why this is such a big stinkin' deal in the second section.

 

YOUR TURN:

Does f( x ) = ( 2 / 3 )x - 5 have an inverse function?

* Just graph it and see if it's one to one.

 

Does f( x ) = 4 - x^( 2 ) have an inverse function?

If it doesn't, fix it so that it does.