`f(x) = cot(x), (0, pi)` Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

We are asked to determine if the function `y=cot(x)` on `(0,pi) `  has an inverse function by finding if the function is strictly monotonic on the interval using the derivative.

`y'=-csc^2(x) ` . On ` (0,pi),-csc^2(x)<0` for all x so the function is monotonic and has an inverse function.

We are asked to determine if the function `y=cot(x)` on `(0,pi) `  has an inverse function by finding if the function is strictly monotonic on the interval using the derivative.

`y'=-csc^2(x) ` . On ` (0,pi),-csc^2(x)<0` for all x so the function is monotonic and has an inverse function.