+23254 f(x) = 3x² - 4x
f(k - x) = 3(k - x)² - 4(k - x) = 3(k² -2kx + kx²) - 4k + 4x = 3k² - 6kx + 3x² - 4k + 4x
for f(x) = f(k - x) --- 3x² - 4x = 3k² - 6kx + 3k² - 4k + 4x
The 3x² on the left side matches the 3x² on the right side, so we can ignore them leaving:
- 4x = 3k² - 6kx - 4k + 4x
On the right side: 3k² - 4k is a constant; there is no equaivalent on the left side, so 3k² - 4k = 0
---> k(3k - 4) = 0 ---> So either k = 0 or 3k - 4 = 0 ---> k = 0 or k = 4/3
What we have left: -4x = -6kx + 4x
-4x = (-6k + 4)x
The only way that this can be true is if -4 = -6k + 4, or k = 4/3
Answer: k = 4/3
