Finding a formula for function f

Question

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!

Answer 1

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*}

Answer 2

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