Find the domain of function $f(x)=\log_2\left(\frac{π+2\sin^{-1}\left(\frac{3-x}{7}\right)}{π}\right)$.
Answer & explanation
Correct answer: option 2
$f(x)=\log_2\left(\frac{π+2\sin^{-1}\left(\frac{3-x}{7}\right)}{π}\right)$
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].