Question

For the function f(x) = 3sin (2x) cos (x), determine whether f(x) is an even function, an odd function, or neither.

A) Even
B) Odd
C) Neither

Answer 1

The function f(x) = 3sin(2x)cos(x) is neither an even function nor an odd function.

Step-by-step explanation:

The function f(x) = 3sin(2x)cos(x) is neither an even function nor an odd function. An even function is one that satisfies f(-x) = f(x) for all x in the domain of the function. An odd function is one that satisfies f(-x) = -f(x) for all x in the domain of the function.

To determine if f(x) is even, we substitute -x for x in the function and simplify: f(-x) = 3sin(2(-x))cos(-x) = -3sin(2x)cos(x).

Since f(-x) is not equal to f(x) for all x, f(x) is not an even function. Similarly, to determine if f(x) is odd, we substitute -x for x in the function and simplify: f(-x) = 3sin(2(-x))cos(-x) = -3sin(2x)cos(x).

Since f(-x) is not equal to -f(x) for all x, f(x) is not an odd function. Therefore, f(x) is neither an even function nor an odd function.