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Question Number 131295 by EDWIN88 last updated on 03/Feb/21

$$Finddomainoffunction$$$$f\left(x\right)=\sqrt{\frac{\cos x-\frac{1}{2}}{6+35x-6x^2}}$$

Answered by liberty last updated on 03/Feb/21

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\frac{\cos \mathrm{x}-1/2}{6+35\mathrm{x}-{6\mathrm{x}}^2}}$$$$\begin{array}{|cc|}\hline \cos \mathrm{x}⩾\frac{1}{2}& {6\mathrm{x}}^2-35\mathrm{x}-6<0\\ -\frac{\pi }{3}⩽\mathrm{x}⩽\frac{\pi }{3}\cup \frac{5\pi }{3}⩽\mathrm{x}⩽\frac{7\pi }{3}& (6\mathrm{x}+1)(\mathrm{x}-6)<0\\ \hline\end{array}$$$$\therefore \mathrm{x}\in (-\frac{1}{6},\frac{\pi }{3}]\cup [\frac{5\pi }{3},6)$$

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