Question

what is the domain and range of the function y= -2cos 1/2 ( x + pi/4 ) -2

Answer 1

If that is cos^(1/2), meaning sqrt(cos), then the domain will be wherever (x+pi/4) >= 0, since sqrt needs a non-negative radicand.

The range of cos(u) is -1 <= y <= 1
range of 2cos(u) is -2 <= y <= 2
range of 2cos(u)-2 = -4 <= y <= 0