# How do you find the domain and range of 2 csc x?

Jul 1, 2018

Domain :  x in RR , x != pi*n ; n is an integer.
Range: $\left(- \infty , 2\right] \cup \left[2 , \infty\right)$

#### Explanation:

$f \left(x\right) = 2 \csc x = 2 \cdot \frac{1}{\sin} x$

Domain: All real number of $x$ except $\sin x = 0$ i.e

values of $x = \pi \cdot n$ for all integers $n$

Domain :  x in RR , x != pi*n ; n is an integer

Range: Since $\csc x$ is reciprocal of $\sin x$ ,

$f \left(x\right) \le - 1 \mathmr{and} f \left(x\right) \ge 1$ for $\csc x$

$f \left(x\right) = 2 \csc x$

$\therefore f \left(x\right) \le - 2 \mathmr{and} f \left(x\right) \ge 2$

Range $\left(- \infty , 2\right] \cup \left[2 , \infty\right)$

graph{2 csc x [-10, 10, -5, 5]} [Ans]