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Are the following functions inverses? \( f(x)=\frac{4}{x-4}-5 \) \( g(x)=\frac{4}{x+5}+4 \) No, they are not inverses Yes, they are inverse

Ask by Coleman Crawford. in the United States
Mar 14,2025

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Yes, they are inverses.

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The Deep Dive

To determine if these functions are inverses, we can check if \( f(g(x)) = x \) and \( g(f(x)) = x \). If both compositions return \( x \), then they are indeed inverses of each other! It’s all about that cozy relationship between the two functions where one undoes the work of the other. To explore further, you can graph these functions using a graphing calculator. If they are inverses, their graphs will be reflections over the line \( y = x \). This visual confirmation adds a fun layer to understanding their relationship, so don't hesitate to grab a graphing tool and see the magic for yourself!

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