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Chapter 1: Problem 2
Find the domain of the function \(f(x)=\sin ^{-1}\left(\frac{1}{\left|x^{2}-1\right|}\right)+\frac{1}{\sqrt{\sin ^{2} x+\sin x+1}}\)
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If \(f(2+x)=f(2-x)\) and \(f(7-x)=f(7+x)\) and \(f(0)=0\), find the minimum number of roots of \(f(x)=0\), where \(20 \leq x \leq 20 .\)
A function \(f:(0, \infty) \rightarrow(2, \infty)\) is defined as \(f(x)=x^{2}\) \(+2\). Find \(f^{-1}(x)\).
Find the domain of the function \(f(x)=\sin ^{-1}\left(\frac{1}{\left|x^{2}-1\right|}\right)+\frac{1}{\sqrt{\sin ^{2} x+\sin x+1}}\)
\(f(x)=x \sin \left(x^{2}+1\right)\)
If \(f(x)=\frac{\sin x+\sin 3 x+\sin 5 x+\sin 7 x}{\cos x+\cos 3 x+\cos 5 x+\cos 7 x}\), then the period of \(f(x)\) is (a) \(\frac{\pi}{4}\) (b) \(\frac{\pi}{3}\) (c) \(\frac{\pi}{2}\) (d) \(\pi\)
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