Question

Is the function of f(x) = |sin(x)| even, odd, or neither?

A) Even
B) Odd
C) Neither
D) Both Even and Odd

Answer 1

A function is said to be even if it satisfies the property f(x) = f(-x) for all x in the domain. On the other hand, a function is odd if it satisfies the property f(x) = -f(-x) for all x in the domain. The function f(x) = |sin(x)| does not satisfy either property, so it is neither even nor odd.

Therefore, the correct answer is: A) Even

Step-by-step explanation:

A function is said to be even if it satisfies the property f(x) = f(-x) for all x in the domain. On the other hand, a function is odd if it satisfies the property f(x) = -f(-x) for all x in the domain. Let's analyze the function f(x) = |sin(x)| to determine whether it is even, odd, or neither.

For the function f(x) = |sin(x)| to be even, it needs to satisfy f(x) = f(-x) for all x in the domain. Let's check:

f(-x) = |sin(-x)| = |-sin(x)|

Since |-sin(x)| is not equal to |sin(x)|, the function f(x) = |sin(x)| is not even.

Next, let's check if the function is odd. For the function f(x) = |sin(x)| to be odd, it needs to satisfy f(x) = -f(-x) for all x in the domain. Let's check:

-f(-x) = -|sin(-x)| = -|-sin(x)| = |sin(x)|

Since |sin(x)| is not equal to -|sin(x)|, the function f(x) = |sin(x)| is not odd.

Therefore, the function f(x) = |sin(x)| is neither even nor odd.