Question

Let $f:[0,2] \rightarrow R$ be the function defined by
$f(x)=(3-\sin (2 \pi x)) \sin \left(\pi x-\frac{\pi}{4}\right)-\sin \left(3 \pi x+\frac{\pi}{4}\right)$ If $\alpha, \beta \in[0,2]$ are such that $\\{x \in[0,2]: f(x) \geq 0\\}=[\alpha, \beta]$, then the value of $\beta-\alpha$ is ______

Answer 1

$\text{The value of}$ $\beta-\alpha$ is $\underline{1}.$