Question

How do you find the domain and range of `2 csc x`?

Answer 1

Domain : `x in RR , x != pi*n ; n` is an integer.
Range: `(-oo,2] uu [2,oo)`

Explanation:

`f(x)= 2 csc x = 2* 1/sin x`

Domain: All real number of `x` except `sin x=0` i.e

values of `x= pi*n` for all integers `n`

Domain : `x in RR , x != pi*n ; n` is an integer

Range: Since `csc x` is reciprocal of `sin x` ,

`f(x) <= -1 or f(x) >=1` for `csc x`

`f(x)= 2 csc x`

`:. f(x) <= -2 or f(x) >=2`

Range `(-oo,2] uu [2,oo)`

graph{2 csc x [-10, 10, -5, 5]} [Ans]