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I need to find a formula for $f(x)$.

The only information about $f$ is:

$\forall x \in {\rm I\!R}, f(\frac{69x}{1+x}) = x^2$

I am clueless about this one.

Thank you for your help!

Billy75
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  • Hint: you know $f(g(x)) = x^2$. Find the inverse $g^{-1}$ of $g$, then $f(g(g^{-1}(x))) = (g^{-1}(x))^2$. – dxiv May 11 '21 at 16:50

2 Answers2

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Substitute $$x=\frac {t}{69-t}$$ Your final answer shall be $f(x)=\left(\frac {x}{69-x}\right)^2$

Shubham Johri
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Ritam_Dasgupta
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HINT

\begin{align*} y = \frac{69x}{1+x} & \Rightarrow y + xy = 69x\\\\ & \Rightarrow x(y - 69) = -y\\\\ & \Rightarrow x = \frac{y}{69 - y} \end{align*}

user0102
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