Question

What are domain and range of these two and how step by step please?​

Answer 1

Explanation:

`\sf f(x) = (1)/(Sin \ x)`

f(x) does not contain values where sin x = 0. Sin x is 0 at integral multiples of π.

Domain = R - nπ , n is integers.

The range of Sin x is [-1 , 1] and in this range we cannot find 1/sin x .

Range = (-∞, -1] U [1,∞)

`\sf f(x) =(1)/(Cos x)`

f(x) does not contain values where Cos x = 0 . Cos x is 0 at integral of multiples of (π/2)

`\sf Domiain =R -((2n+1)\pi )/(2)`

The range of Cos x is [-1,1] and in this range we cannot find 1/Cos x.

Range = (-∞, -1] U [1,∞)