Question

The domain of the function $y=\sqrt{\sin x+\cos x}+\sqrt{7x-x^2-6}$ is

Answer 1

$y=\sqrt{\sin x+\cos x}+\sqrt{7x-x^2-6}$

For Domain $(\sin x+\cos x)\ge 0$ and $(7x-x^2-6)\ge 0$

$\sin (\pi +\frac{\pi }{4})\ge 0x^2-7x+6\le 0$

Thus $(x-6)(x-1)\ge 0$

$n\in I,n\pi \le x+\frac{\pi }{4}\le (2n+1)\pi 1\le x\le 6$

$n\in I,(n-\frac{1}{4})\le x\le (2n+\frac{3}{4})\pi$

Taking Intersection of these two sets

We get $1\le x\le 6$