Given:

Need to find: Where the functions are defined.

The maximum value of an angle is 2π

So, the maximum value of x = 2π/3.

Whereas, the minimum value of x is 0

Therefore, the domain of the function, D_f(x) = (0, 2π/3).

Now, the minimum value of sinθ = 0 and the maximum value of sinθ = 1. So, the minimum value of the denominator is 1, and the maximum value of the denominator is 2.

Therefore, the range of the function, R_f(x) = (1/2, 1).