F.6函數較深問題

f(2 - cosx) = cos 2x - cos xf(2 - cosx) = (2cos²x - 1) - cos x
令 2 - cos x = y - 1
則 cos x = 3 - y , 代入上式得
f(y - 1)
= (2(3 - y)² - 1) - (3 - y)
= 2y² - 12y + 18 - 1 - 3 + y
= 2y² - 11y + 14
= (2y - 7)(y - 2)
即 f(x - 1) = (2x - 7)(x - 2)