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Inverse Functions

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if f(x)=2x/x-5,

find f^-1(x).

May 18, 2018

#1
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if f(x)=2x/x-5,

find f^-1(x).

That is a bit better :)

You have written

$$if\\ f(x)=\frac{2x}{x}-5\\ find \;\;f^{-1}(x).$$

But I expect you left out the brackets and you actually mean

$$if\\ f(x)=\frac{2x}{x-5}\\ find \;\;f^{-1}(x).$$

Be careful with those brackets.

Let

$$​​​​y=\frac{2x}{x-5}\\ \text{x cannot be 5}\\ \text{Now make x the subject}\\ yx-5y=2x\\ yx-2x=5y\\ x(y-2)=5y\\ x=\frac{5y}{y-2}\\ \text{Now for the inverse swap x and y over}\\ y=\frac{5x}{x-2}$$

So if

$$f(x)=\frac{2x}{x-5}\\then\\ f^{-1}(x)=\frac{5x}{x-2}\\ where\;\;x\ne2$$

Here are the graphs

The inverse fof a funtion is the reflection of the funtion in the line y=x

NOW LEARN FROM THIS AND TRY AND DO THE REST BY YOURSELF!

May 18, 2018