WEBVTT
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all right, we're going to find the inverse of
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this function, and the first thing I like to
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do is just call f of X y. So
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we have y equals four X minus 1/2 X plus
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three. Now for the inverse we need to interchange
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or switch X and y So we have X equals
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before. Why minus 1/2 y plus three. Now
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we want to isolate Why So let's multiply both sides
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by the denominator. Two y plus three and we
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have x times a quantity two y plus three equals
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four y minus one. Now we can distribute the
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X to get rid of the parentheses, and we
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have two x y plus three X equals four y
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minus one. Remember, our goal here is to
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isolate Why, So we need to get the white
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terms on one side of the equation and the other
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terms on the other side. So I'm going to
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subtract four wife from both sides, and I have
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two x y minus four y, and I'm going
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to subtract three x from both sides. So this
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equals negative one minus three x. All right now
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, it's factor. Why out of both terms on
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the left and we have why Times a quantity two
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X minus four equals negative one minus three x.
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Finally, we can divide both sides by two x
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minus four. So we have y equals negative one
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minus three x over two X minus four. Now
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it looks a little bit better with fewer negative signs
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if we multiply the top by negative one and the
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bottom by negative one. So that would be one
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plus three x over four minus two x It's equivalent
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. It just looks a little more slick. And
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finally, let's go ahead and rename this instead of
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calling it Why, let's call it F inverse of
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X. Make a little more space here F and
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bursts of X. There we go.