Question

Which of the following represents the domain and range of y = CSC X?

Answer 1

Given:

`y=\csc x`

To find:

Domain and range of given function

Step-by-step explanation:

As y = csc(x) is reciprocal of y = sinx. So, its domain and range is related to sine's domain and range.

The domain of y = csc (x) is every value in the domain of sine with exception of where

sinx = 0. Since the reciprocal of 0 is undefined. so,

The domain of y = csc(x) is,

`x\in R,x\\e\pi.n,\text{ n}\in Z`

Since the range of y = sin (x) is -1 ≤ y ≤ 1. we get that the range of y = csc(x) is,

`y\leq-1\text{ or }y\ge1`

Final answer:

Hence, the correct option is (D).