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sin(x)-cos(x) = (1)sin(x)+(-1)cos(x) so the range is sqrt((1)^2+(-1)^2)=1 and the domain is R <><><><><> The domain of sin x - cos x is [-infinity, +infinity]. The range of sin x - cos x is [-1.414, +1.414].
if y = x2 + 1 Then the minimum value of y is 1, which happens at the point (0, 1). It lies in the domain of real numbers. i.e. {y | y ≥ 1, y ∈ ℝ}
The domain of y = 1/x2 is all numbers from -infinity to + infinity except zero. The range is all positive numbers from zero to +infinity, except +infinity.
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The range of cosine is [-1, 1] which is, therefore, the domain of cos-1. As a result, cos-1(2) is not defined.