Question

The function y = x/tan(x) is _______. An even, an odd, neither an even nor an odd. Function, and the function y = sec(x)/x is ... an even, an odd, neither an even nor an odd.

A) Even, Even
B) Odd, Odd
C) Neither, Neither
D) Even, Odd

Answer 1

The function y = x/tan(x) is neither an even nor an odd function, while the function y = sec(x)/x is an even function.

Step-by-step explanation:

The function y = x/tan(x) is neither an even nor an odd function. An even function satisfies the property f(-x) = f(x), meaning that the function remains unchanged when we replace x with -x. Similarly, an odd function satisfies the property f(-x) = -f(x), meaning that the function changes sign when we replace x with -x. In the given function y = x/tan(x), neither of these properties hold true. Therefore, it is neither an even nor an odd function.

The function y = sec(x)/x is an even function. An even function satisfies the property f(-x) = f(x), meaning that the function remains unchanged when we replace x with -x. In the given function y = sec(x)/x, if we replace x with -x, the value of sec(x) remains the same since sec(-x) = sec(x), while the value of x remains the same as well. Thus, the function is even.