Find domain of cos^2x -1 and cos(x^2-1)?

Question

Find domain of cos^2x -1 and cos(x^2-1)?

Answer 1

A) cos^2(x) -1

the domain of cos(x) is [-1,1].  the domain of cos^2(x) is [0,1], so the domain of cos^2(x)-1 is [-1,0]

B) cos(x^2-1)

the domain of (x^2-1) is [-1, inf].  since cos(x) is periodic, the range of cos(x^2-1) is the same as cos(): [-1, 1]