Find the domain of the function $f ( x ) = \frac { x } { - 2 \sin x - 3 }$.
A) $( - \infty , \infty )$
B) $\left[ - \frac { 3 } { 2 } , \infty \right)$
C) $[ - 3 , - 2 ]$
D) $[ 2,3 ]$

Question

Quizplus · Accepted Answer

The domain of $f(x) = \frac{x}{-2\sin x - 3}$ is all real numbers, $(-\infty, \infty)$, because the only restriction would be values of $x$ that make the denominator zero. However, since $-2\sin x - 3$ can never be zero (as $-2\sin x$ ranges between -2 and 2, making the whole expression range between -5 and -1), there are no restrictions on $x$.

Find the Domain of the Function f(x)=x−2sin⁡x−3f ( x ) = \frac { x } { - 2 \sin x - 3 }f(x)=−2sinx−3x​

Find the Domain of the Function $f ( x ) = \frac { x } { - 2 \sin x - 3 }$