Intersections satisfy g(x)=x−cos x=0. Any root lies in [−1,1]. On that interval $g\prime=1+\sin x>0$, so there is at most one root. Since g(0)=−1 and g(1)>0, continuity ensures one root. Therefore the count is 1.
More Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration questions
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