Day: October 11, 2017

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: