Question

What is the domain and range of `sin x + cos x`?

Answer 1

Domain:`x+pi/4 in (-oo, oo) to x in (-oo, oo)`

Range:`sqrt 2 [-1, 1] = [-sqrt 2, sqrt 2]`. Illustrative graph is inserted

Explanation:

graph{cos x + sin x [-10, 10, -5, 5]} #cos x + sin x=sqrt2(sin(pi/4)cos

x+cos(pi/4)sin x)=sqrt2sin(x+pi/4)#

Domain:`x+pi/4 in (-oo, oo) to x in (-oo, oo)`

Range: `sqrt 2 [-1, 1] = [-sqrt 2, sqrt 2]`.