Question

algebraically, determine whether the following is even, odd, or neither. F(x) = x^3-2x+3

Answer 1

To determine if the function is even, odd, or neither, we need to check if f(-x) = f(x) for all x in the domain.

Let's first find f(-x):

f(-x) = (-x)^3 - 2(-x) + 3
f(-x) = -x^3 + 2x + 3

Now let's compare f(-x) to f(x):

f(-x) = -x^3 + 2x + 3
f(x) = x^3 - 2x + 3

Since f(-x) is not equal to f(x) for all x in the domain, the function is neither even nor odd.