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# Functions help

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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

### 1+0 Answers

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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