Question

What is the range of F(x) = -4cos2x?

Answer 1

Assuming you want the range of
   -4cos(2x)

the range of the cosine function is -1 to 1. When that is scaled by a factor of -4, it becomes 4 to -4.

The range of F(x) is [-4, 4] in interval notation.


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If you want the range of 
   F(x) = -4cos²(x)
that range will be -4×[0, 1] = [-4, 0].