Answer:
C
Step-by-step explanation:
We are given that a function
[tex]f(x)=4csc(x)[/tex]
Domain of function f(x)={x\x[tex]\neq n\pi,n\in Z[/tex]}
Range of function,f(x)=([tex]-\infty,-4]\cup [4,\infty)[/tex]
Substitute x=[tex]\frac{\pi}{2}[/tex]
[tex]f(\frac{\pi}{2})=4csc(\frac{\pi}{2})=4[/tex]
[tex]csc(\frac{\pi}{2})=1[/tex]
Substitute x=[tex]-\frac{\pi}{2}[/tex]
[tex]f(-\frac{\pi}{2})=4csc(-\frac{\pi}{2})=-4[/tex]
[tex]csc(-\frac{\pi}{2})=-1[/tex]
Substitute x=0,[tex]\pm\pi,\pm 2\pi,[/tex]..
[tex]f(0)=\infty=f(\pi)=f(2\pi)=[/tex]...
[tex]f(-\pi)=-\infty=f(-2\pi)=[/tex]...
Hence, option C is true.
