Find the domain of function $f(x)=\log_2\left(\frac{π+2\sin^{-1}\left(\frac{3-x}{7}\right)}{π}\right)$.

[-4, 10]

$f(x)=\log_2\left(\frac{π+2\sin^{-1}\left(\frac{3-x}{7}\right)}{π}\right)$

Least value of $2 \sin^{-1}\left(\frac{3-x}{7}\right)$ is '-2' for which $\frac{π+2\sin^{-1}\left(\frac{3-x}{7}\right)}{π}$ is positive. 

So, for domain we must have $-1≤\frac{3-x}{7}≤1$

$∴-7≤3-x≤7$

$⇒-10≤-x≤4$

$⇒-4≤x≤10$

Thus, domain of f(x) is [-4, 10].