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anonymous
 5 years ago
for what type of function will {g(f(x))}and {f(g(x))} both equal to x? explain.
anonymous
 5 years ago
for what type of function will {g(f(x))}and {f(g(x))} both equal to x? explain.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0When one is the inverse of the other.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Take the first case, g(f(x)). You take x and f maps it to f(x). You're wanting g now such that g will take that result and send it back to x (i.e. undo the operation). The function that will do that is the inverse of the original function.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is the definition of an inverse function.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Example, \[f(x)=e^x , g(x) = \ln x\]then\[f(g(x))=e^{\ln x}=x\]by definition of logarithm, and\[g(f(x))=\ln e^x = x \ln e = x \]by log laws. The two functions,\[f(x)=e^x , g(x)=\ln x\]are inverse to each other. There is an infinity of such functions.
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