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Let's look at another example:

With the two previous things in mind, can you draw the inverse of this?

g( x ) = square root( x )

Since we don't know what the graph ofg( x ) = square root( x )looks
like yet (well, I do... but you don't), let's plot a few points:

 

x : 0 , 1 , 4 , 9 ... y : 0 , 1 , 2 , 3

a graph of g( x ) ... it includes the points ( 0 , 0 ) , ( 1 , 1 ) and ( 4 , 2 )

It's just a half a parabola
lying on its side!

Cool!  So, what are the two things?

1 )They are symmetric with respect to y = x
 
2 )Every (x, y) has a (y, x) partner

Now, you can graph the inverse!

 
a graph of f( x ) and g( x ) ... they are mirror images across the line y = xHey!  It's half of
Standard Parabola Guy!

f( x ) = x^2

 

Now, I can tell you why I saidx is greater than or equal to 0 for these guys in the last
lesson!

 

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