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Determine the equation of the inverse function.$$f(x)=\frac{11-3 x}{2 x+5}$$

$f^{-1}(x)=\frac{11-5 x}{3+2 x}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

McMaster University

Baylor University

University of Michigan - Ann Arbor

Lectures

03:46

Find the inverse function …

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Finding Inverse Functions …

so before we actually try to look for this in verse. One of the things you should check is to make sure that this is a 1 to 1 function. So you can either do that by graphing using the horizontal line test or just by taking the derivative. And you'll see, uh, this is always increasing or always decreasing. But I'm just gonna kind of pretend like we did that and just go ahead and solve for this, Um, because we really won't have any issues with it, Kind of like we did with, like, the square roots. So the first thing we need to do is just interchange X and y. So the X is equal to 11 minus three x three y all over two y plus five. Um, multiply across maybe two x y plus five x busy. Go to 11 minus three y. Now we can go ahead and collect our wise on the same side. So two x y plus three y is equal to 11 minus five X Uh oh. Factor at the Y on the left, so B Y is equal to two X plus three and then we can go in and divide that over. So that gives us Y is equal to 11 minus five x all over two X plus three, which this is just f inverse of X.

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