Determine whether the function is even, odd, or neither.
$f ( x ) = x \csc \frac { x } { 2 }$
A) Odd
B) Neither
C) Even

Question

Determine whether the function is even, odd, or neither. 
$f ( x ) = x \csc \frac { x } { 2 }$
A) Odd
B) Neither
C) Even

Quizplus · Accepted Answer

We need to check whether the given function satisfies the conditions for even or odd functions.

For even functions, we should have f(-x) = f(x) for all x.

For odd functions, we should have f(-x) = -f(x) for all x.

Let's first check whether the function is even.

f(-x) = (-x) * csc(-x/2)

= -x * csc(x/2)

= -f(x)

Therefore, the function is odd.

Determine Whether the Function Is Even, Odd, or Neither f(x)=xcsc⁡x2f ( x ) = x \csc \frac { x } { 2 }f(x)=xcsc2x​