anonymous
  • anonymous
for what type of function will {g(f(x))}and {f(g(x))} both equal to x? explain.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
When one is the inverse of the other.
anonymous
  • anonymous
y
anonymous
  • anonymous
Take 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.

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anonymous
  • anonymous
This is the definition of an inverse function.
anonymous
  • anonymous
Example, \[f(x)=e^x , g(x) = \ln x\]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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