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

 

find f^-1(x).

 

smileysmileysmiley

 May 18, 2018
 #1
avatar+100173 
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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

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