Answer:
0 < f(x) ≤ 3/4, or (0, 3/4]
Step-by-step explanation:
x² - x + 1 = x² - x + 1/4 + 3/4 = (x - 1/2)² + 3/4
It is always positive and has a minimum value of 3/4 at x = 1/2
So f(x) is always positive (not equal zero) and has a maximum value of 3/4
Then the range is 0 < f(x) ≤ 3/4, or (0, 3/4]
