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

Isf( x ) = x^( 2 )one-to-one?
a graph of f( x ) = x^( 2 ) ... it does not pass the horizontal line testNo!  It fails the horizontal line test.
Sof( x ) = x^( 2 )does NOT
have an inverse function.

Hey!  Wait just a darn minute there, Skippy!

Did I just say that f( x ) = x^( 2 )does NOT have an inverse
function?

Yep, that's what I said.

But, didn't I say that the inverse of f( x ) = x^( 2 )was
g( x ) = square root( x )?  

Nope!  Not quite!