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Q.
Part of the domain of the function $f(x)=\sqrt{\frac{\cos x-1 / 2}{6+35 x-6 x^2}}$ lying in the interval $[-1,6]$ is
Relations and Functions
Solution:
The function $f$ is meaningful only if $\cos x-1 / 2$ $\geq 0,6+35 x-6 x^2>0$ or $\cos x-1 / 2 \leq 0,6+35 x-6 x^2< 0$
i.e., $\cos x \geq 1 / 2,(6-x)(1+6 x)>0$ or $\cos x \leq 1 / 2$, $(6-x)$ $(1+6 x)< 0$.
These inequalities are satisfied if $x \in(-1 / 6, \pi / 3] \cup[5 \pi / 3,6)$.