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$93-94=$ Inverse Functions A function $f(x)$ is given. (a) Findthe domain of the function $f$ . (b) Find the inverse function of $f .$$$f(x)=\ln (\ln (\ln x))$$

a) $D_{f}=(e,+\infty)$b) $f^{-1}(x)=e^{e^{x^{x}}}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Campbell University

McMaster University

Harvey Mudd College

Lectures

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Inverse Functions A functi…

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Find the inverse of the fu…

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Inverse Functions(a) F…

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the function $f$ is one-to…

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In Problems $63-74,$ the f…

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Inverse Function Property …

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so to find the domain of this problem are of this function. What we can do is look at the outermost after log function and so we want to look at the inside of the outermost natural law function. So we have natural log of X, or rather, the natural log of the natural. Lagerback's is equal to zero so we can find where this value gives us zero. So so way would have e to the zero we would have e to be to. The zero is equal to one and so one is equal to the natural log of X. So now we can solve for this so we would have e to the one is equal to x So access equal to E and this gives us this gives us zero for the inside of our function. Well, then, if X is greater than zero or right Rather, if X is greater than e so this is X is equal to e. And if X is greater than E, then our than our f of X is R f of X works. In other words, in other words, are Ln of al Innovex is greater than is greater than zero is greater than is your So our domain here is from E to infinity from me too and 50. And so now we confined our inverse function. So So this would be X is equal to the natural log of the natural log of the natural. Long of why Why? And so So we can say Well, e to the e to the X is equal to the natural log of the natural law. Goodbye. So we can do this again. So we would have e to the e to the X is equal to the natural log of y. And then doing this one last time gives us e to the to the to the X is equal to why and so this here is our inverse function. This is our inverse function.

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