Question

Part of the domain of the function $f(x)=\sqrt{\frac{\cos x-1/2}{6+35x-6x^2}}$ lying in the interval $[-1,6]$ is

• A. $[-1/6,\pi /3]\cup [5\pi /3,6]$
• B. $(-1/6,\pi /3]\cup [5\pi /3,6)$
• C. $(-1/6,6)$
• D. none of these

Answer 1

Answer: (A)

The function $f$ is meaningful only if $\cos x-1/2$ $\ge 0,6+35x-6x^2>0$ or $\cos x-1/2\le 0,6+35x-6x^2<0$
i.e., $\cos x\ge 1/2,(6-x)(1+6x)>0$ or $\cos x\le 1/2$, $(6-x)$ $(1+6x)<0$.
These inequalities are satisfied if $x\in (-1/6,\pi /3]\cup [5\pi /3,6)$.