To determine if the function f(x) = 9 – 4x² is an odd function, we can use the definition of odd functions. A function f is considered odd if for every x in the domain of f, the following condition holds: f(-x) = -f(x).
To check this for our function, we first find f(-x):
f(-x) = 9 – 4(-x)² = 9 – 4x²
Now we compare this to -f(x):
-f(x) = -(9 – 4x²) = -9 + 4x²
Next, we see if f(-x) is equal to -f(x):
f(-x) = 9 – 4x²
-f(x) = -9 + 4x²
Since they are not equal (9 – 4x² ≠ -9 + 4x²), we conclude that the function does not satisfy the condition for being an odd function. Therefore, we can say that f(x) = 9 – 4x² is not an odd function.