Introduction:
To determine the interval of the set S for the function f:R→S, we need to analyze the range of values that the function can take. In other words, we need to find the range of the function f(x) = sin(x) - √3cos(x).

Analysis of the function:
Let's analyze the given function f(x) = sin(x) - √3cos(x) in detail.

Step 1: Simplify the function:
We can simplify the function using trigonometric identities. Recall that sin(π/3) = √3/2 and cos(π/3) = 1/2.

f(x) = sin(x) - √3cos(x)
= sin(x) - √3cos(x)
= sin(x) - √3(cos(x)/1)
= sin(x) - √3(cos(x)/cos(π/3))
= sin(x) - √3(tan(π/3)sec(x))
= sin(x) - √3(tan(π/3)csc(x))

Step 2: Simplify further:
Using the identity tan(π/3) = √3, we can simplify the function further.

f(x) = sin(x) - √3(tan(π/3)csc(x))
= sin(x) - √3(√3csc(x))
= sin(x) - 3csc(x)

Step 3: Determine the range of the function:
To determine the range of the function, we need to find the maximum and minimum values that the function can take.

Maximum value:
The maximum value of sin(x) is 1, and the maximum value of csc(x) is 1 when sin(x) = 1. Therefore, the maximum value of the function f(x) = sin(x) - 3csc(x) is 1 - 3(1) = -2.

Minimum value:
The minimum value of sin(x) is -1, and the minimum value of csc(x) is -1 when sin(x) = -1. Therefore, the minimum value of the function f(x) = sin(x) - 3csc(x) is -1 - 3(-1) = 2.

Conclusion:
The range of the function f(x) = sin(x) - 3csc(x) is [-2, 2]. Therefore, the interval of the set S for the function f:R→S is [-2, 2].