Question

Determine whether the function f(x) = -1+2x-x^2 is even, odd or neither

Answer 1

To determine whether the function f(x) = -1+2x-x^2 is even, odd, or neither, we need to evaluate its properties when inputting -x and x, respectively.

For an even function, we must have f(-x) = f(x) for all x in the domain of f. Let's check:

f(-x) = -1 + 2(-x) - (-x)^2
= -1 - 2x - x^2

f(x) = -1 + 2x - x^2

Since f(-x) is not equal to f(x), the function is not even.

For an odd function, we must have f(-x) = -f(x) for all x in the domain of f. Let's check:

-f(x) = -(-1 + 2x - x^2)
= 1 - 2x + x^2

f(-x) = -1 + 2(-x) - (-x)^2
= -1 - 2x + x^2

Since f(-x) is equal to -f(x), the function is odd.

Therefore, the function f(x) = -1+2x-x^2 is odd.