Question

Find the value of $x$ for which $f\left(x\right)=\sqrt{\sin x-\cos x}$ is defined, $xϵ[0,2\pi ]$

• A. $xϵ[\frac{\pi }{8},\frac{5\pi }{8}]$
• B. $xϵ[\frac{\pi }{4},\frac{3\pi }{4}]$
• C. $xϵ[\frac{\pi }{6},\frac{5\pi }{6}]$
• D. $xϵ[\frac{\pi }{4},\frac{5\pi }{4}]$

Answer 1

The correct option is D $xϵ[\frac{\pi }{4},\frac{5\pi }{4}]$

$f\left(x\right)=\sqrt{\sin x-\cos x}$ is defined if $\sin x\ge \cos x$
From the graph, $\sin x\ge \cos x$, for $xϵ[\frac{\pi }{4},\frac{5\pi }{4}]$