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How would you find the inverse function of $f(x)=e^{x/2}$?

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    This is the same as setting $y = e^{x/2}$, and then solving for $x$ in terms of $y$. Are you familiar with how that is done? (Hint: logarithms)2012-10-30
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    *Real-valued..* $f(x) = e^{g(x)} \iff \log f(x) = g(x).$2012-10-30

2 Answers 2

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$$y = \exp(x/2) \implies \log_e(y) = \log_e(\exp(x/2)) = x/2 \implies x = 2 \log_e(y)$$

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    this is wrong abswer2012-10-30
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    @AdiDani: No, it's not. $\log_e$ is the same thing as $\ln$.2012-10-31
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    @Hans Lundmarkt. It is wrong in sense that $x=2\log_e(y)$ is not inverse but needs to interchange x and y to $y=2\log_e(x)$2012-10-31
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    @AdiDani: The answer gives $x=f^{-1}(y)$ instead of $y=f^{-1}(x)$. So what? It's the same function $f^{-1}$ no matter what variables you use for writing it.2012-10-31
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$$f(x)=y=e^{\frac{x}{2}}$$ inverse is $x=e^{\frac{y}{2}}\iff\ln x=\ln e^{\frac{y}{2}}\iff \ln x =\frac{y}{2}\iff y=2\ln x$