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Definition of Inverse - Problem 2

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Inverse application: For this particular example behind me what I know is a function that f(x) is equal 2to the x and I’m trying to find the value of an inverse. 2 to the x may be a new function to you, that’s okay we’re going to talk about it later, but what you do need to know is that it is a one to one function so it does have an inverse so this application does hold true.

What we’re trying to find is f inverse of 8. In dealing with function notation what’s in the parenthesis is our x value. What this is actually telling us is we have a point 8, something on our inverse. What we’re trying to find is what this blank is. If we have the inverse for that point we can take, switch the x and ys in order to find the point on the normal function.

If we add the point 8, something on our inverse, we now know that we have the point something, 8 on our function. We want the value of 8 to come out here. So just thinking about 2 to what power is going to give us 8? We have trouble with that transition this is our y value, f(x) is the same as our y values so this is really turning it into 8 is equal to 2 to the x. Just think about what power of 2 will give us 8, hopefully you can remember your powers and this comes out to be 3. 2 to the third is equal to 8 so we know that we have the point 3,8 on our function which corresponds to the point 8,3 on our inverse. So we’re just going a little bit backwards, taking one point in our inverse switching it over to our function we can solve this out to get our answer.

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