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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.

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  1. anonymous
    • 5 years ago
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    When one is the inverse of the other.

  2. anonymous
    • 5 years ago
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    y

  3. anonymous
    • 5 years ago
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    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.

  4. anonymous
    • 5 years ago
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    This is the definition of an inverse function.

  5. anonymous
    • 5 years ago
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    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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