Is the function f(x)=x²(4-x)²
even?
if x = -1
(4-x)^2 = 25
if x = +1
(4-x)^2 = 9
so it is not the same for all + x as for all -x so it is not even.
I answered odd and the instuctor marked it wrong, would it be neither?
It is also not odd.
To determine whether a function is even or not, we need to check if it exhibits symmetry with respect to the y-axis.
For a function to be even, it must satisfy the condition f(x) = f(-x) for all values of x.
Let's check if the function f(x) = x²(4-x)² satisfies this condition:
1. Substitute (-x) for x in the function expression:
f(-x) = (-x)²(4-(-x))²
Simplifying, we get: f(-x) = x²(-4+x)²
2. Compare f(x) and f(-x):
f(x) = x²(4-x)²
f(-x) = x²(-4+x)²
As we can see, f(x) and f(-x) are not equal. Therefore, the function f(x) = x²(4-x)² is not even.