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If \($f(x)=\dfrac{a}{x+2}$\), solve for the value of a so that \(f(0)=f^{-1}(3a)\).

 May 5, 2018
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To get f-1 rewrite f as:

 

   \(f=\frac{a}{x+2}\\x+2=\frac{a}{f}\\x=\frac{a}{f}-2\)

 

Now change f into x and x into f-1:

\(f^{-1}=\frac{a}{x}-2\)

 

We have: \(f(0)=\frac{a}{2}\text{ and }f^{-1}(3a)=\frac{a}{3a}-2\rightarrow-\frac{5}{3}\)

 

I'm sure you can take it from here!

 May 5, 2018

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