Question

For the following exercises, determine whether the function is even, odd or neither f(x)= -5 /x2 9x6

Answer 1

A function is neither even nor odd if it doesn't satisfy the conditions for even or odd functions. In this case, the function f(x) = -5/(x^2+9x+6) is neither even nor odd.

Step-by-step explanation:

A function is even if it satisfies the condition f(x) = f(-x) for all values of x in the domain. A function is odd if it satisfies the condition f(x) = -f(-x) for all values of x in the domain.

In this case, the function f(x) = -5/(x^2+9x+6) is neither even nor odd. To determine this, we need to check whether f(x) = f(-x) and f(x) = -f(-x) hold.

By substituting x with -x, we get f(-x) = -5/((-x)^2+9(-x)+6) = -5/(x^2-9x+6).

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