Question

Let f(x)=cos(x)/(1+x²) Determine from the graph if f is even, odd, or neither.

Answer 1

The function f(x) = cos(x)/(1+x²) is neither even nor odd.

Step-by-step explanation:

The function f(x) = cos(x)/(1+x²) is neither even nor odd. To determine this, we need to check if f(-x) = f(x) and if f(-x) = -f(x). Let's evaluate:

f(-x) = cos(-x)/(1+(-x)²) = cos(-x)/(1+x²) = cos(x)/(1+x²) = f(x)

Since f(-x) is equal to f(x), the function is not odd. Now let's evaluate:

f(-x) = cos(-x)/(1+(-x)²) = cos(-x)/(1+x²) = -cos(x)/(1+x²) = -f(x)

Since f(-x) is equal to -f(x), the function is not even either. Therefore, f(x) is neither even nor odd.