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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 .$$$f(x)=\log _{2}\left(\log _{10} x\right)$$

a) $D_{f}=(1,+\infty)$b) $f^{-1}(x)=100^{x}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Missouri State University

McMaster University

University of Michigan - Ann Arbor

Lectures

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Inverse Functions A functi…

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For each function, determi…

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Find the inverse of the fu…

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Inverse Functions(a) F…

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? Inverse Functions Find t…

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Find the inverse of each f…

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Inverse Function Property …

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For the following exercise…

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the function $f$ is one-to…

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Find the inverse function …

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in Inverse Function Proper…

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So you want to find the domain of F here? Well, we have to look at the inside of our outermost longer than function. So in other words, we have to say that log based 10 of X we confined where this is equal to this is equal to zero. So if we convert this to exponential form, we have 10 to the zero is equal to X. In other words, X is equal to one. So if X is greater than one, then this means our log based 10 of X is greater than zero. So we know that that our domain here is greater than one. So our domain or FX is from one to infinity. And so now we confined the the inverse function. Well, if we if we replace our X with y So in other words, we have X is equal to log of to long base to of log based 10 of 10 of X. Well, we have our base to so we can convert this to exponential form. So we have to to the to the X is equal to log based 10 of X and so we can we can do this further and so we have 10 to the to the to to the X to to the X this is equal to this is equal to Or we would have wide here. This should. This should be why? Since we flipped our exes, we we changed all the access to wise and all of our wise to access. So this meat, they should be Why there should be why And so now solving for why we have 10 to the two X is equal to why is equal to what and so So this is our This is our inverse function. This is our in gris function and this remember, it was our domain of the original function. And so this is our inverse function.

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