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(a) Let the domain of f be all reals numbers, be defined by f(x) = x - 1/x. Show that f has no inverse function WITHOUT GRAPHING/USING THE HORIZONTAL LINE TEST.

 

(b) Let the domain of g be (0, inf), be defined by g(x) = x - 1/x. Show that g has an inverse function WITHOUT GRAPHING.

 

PLEASE HELP ASAP! THANKS!

 May 9, 2021
 #1
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If you plot the graph, you will find that the any horizontal line intersects the graph at most once.  So by the horizontal line test, the function has an inverse.

 May 9, 2021
 #2
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Umm.... thanks for your answer but you know the question clearly says not to use graphing, right? 

Guest May 9, 2021

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