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anonymous
 5 years ago
given f(x)=In(x) and g(x)=e^x, determine f(g(x)). What does this tell you about the relationship between In(x) and e^x?
anonymous
 5 years ago
given f(x)=In(x) and g(x)=e^x, determine f(g(x)). What does this tell you about the relationship between In(x) and e^x?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0To determine f(g(x)), you substitute g(x) everywhere there is an x in f(x). Since f(x)=ln(x), f(g(x))= ln(g(x))= ln(e^x). Using the laws of logarithms, you can move the x in the exponent in front of of the logarithm, so it reads x*ln(e). But the natural log of e is just 1, so we can conclude that f(g(x))=x. This special relationship indicates that f(x) and g(x) are inverse functions. (This happens whenever f(g(x))=x.)
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