Question

What is the domain and range of `f(x)=2sin(x+pi)-4`?

Answer 1

Domain: `RR`
Range: `[-6,-2] in RR`

Explanation:

`sin(x+pi)` is defined for all Real values of `x`
therefore `2sin(x+pi)-4` is defined for all real values of `x`
`rArr` Domain `= RR`

`sin(theta)` for all `theta in RR` (including `theta=x+pi`) has a Range of `[-1,+1]`
therefore `2sin(x+pi)` has a Range of `[-2,+2]`
and
`2sin(x+pi)-4` has a Range of `[-2-4,+2-4] = [-6,-2]` (in `RR`)