Book: RS Aggarwal - Mathematics
Chapter: 3. Functions
Subject: Maths - Class 11th
Q. No. 15 of Exercise 3C
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15
Find the domain and the range of each of the following real function: 
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, Df(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, Rf(x) = (1/2, 1).
