# Talking inverse functions with my older son

My older son was stuck on a question about inverse functions from his Precalculus book:

Let $f(x) = \frac{cx}{2x + 3}$

Assume that $f(f(x)) = x$ for all $x \neq -3/2$. Solve for $c$.

We began by talking about what was giving him difficulty and then moved on to solving the problem.

Next we moved on to looking at the function on Mathematica. It was a little unlucky that the scale was different for the x- and y-axes, but I think the pictures still got the point across.

After we finished talking I posted about the problem on twitter and John Golden made a neat Desmos version of the problem: