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The graph now passes the horizontal line test and we do have an inverse: Note how each graph reflects across the line y = x onto its inverse. So how is it that we arrange for this function to have an inverse? We consider only one half of the graph: x > 0.
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f(2) = 4 and f(-2) = 4 so what is an inverse function supposed to do with 4? By definition, a function cannot generate two different outputs for the same input, so the sad truth is that this function, as is, does not have an inverse. Consider the graph of Note the two points on the graph and also on the line y=4.Do you know what is wrong? Congratulations if you guessed that the top function does not really have an inverse because it is not 1-1 and therefore, the graph will not pass the horizontal line test. But something is not quite right with this pair. Let us begin with a simple question: What is the first pair of inverse functions that pop into YOUR mind? This may not be your pair but this is a famous pair.