Precalc0108to0109-page19 - undoes what the (restricted)...

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(Section 1.9: Inverses of One-to-One Functions) 1.9.9 The graph of g , or y = gx () , is in blue below. It passes the HLT , meaning that g is one-to-one. Therefore, when we reflect the graph about the line y = x (drawn as a dashed line, though it is not an asymptote), we obtain the red graph of y = g ± 1 x () below, and it passes the VLT . It should look familiar …. . • The graph of y = g ± 1 x () is the graph of y = x , because g ± 1 x () = x . It makes sense that the corresponding square root function
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Unformatted text preview: undoes what the (restricted) squaring function does. It is also the graph of x = g y ( ) , or x = y 2 , with y restricted to 0, ) . This is consistent with the aforementioned Graphical Properties of Inverse Functions. The graph of x = g y ( ) for a function g is the reflection of the graph of y = g x ( ) about the line y = x . This holds even if g is not one-to-one....
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