math problem hard to solve

Question

 Determine if the following functions are one-to-one, even,odd, periodic.

 f(x)=cos(9x) for x∈R

please tell me the right answer so I can understand properly

Answer 1

For x∈R this function is not one-to-one, because for example equation cos9x = 0 has infinitly many solutioms:

9x = π/2 + kπ, or x = π/18 + kπ/9, k∈Z.

F9x) is even function, because f(-x) = cos(-9x) = cos9x = f(x0.

f(x) is periodic with period 2π/9