The domain of the function f(x) = cos^-1((x^2-5x + 6)/(x^2-9))/(log e(x^2 - 3x + 2)) is

Question

The domain of the function f(x) = \(\cfrac{cos^{-1}(\frac{x^2-5x+6}{x^2-9})}{log_e(x^2-3x+2)}\) is

cos^-1((x² - 5x + 6)/(x² - 9))/(log e(x² - 3x + 2))

(A) (-∞, 1) U (2, ∞)

(B) (2, ∞)

(C) [-1/2, 1) U (2, ∞)

(D) [-1/2, 1) U (2, ∞) - {\(\frac{3+\sqrt5}2,\frac{3-\sqrt5}2\)}

Answer 1

Correct answer is (D)  [-1/2, 1) U (2, ∞) - {\(\frac{3+\sqrt5}2,\frac{3-\sqrt5}2\)} 

after taking intersection of each solution

[-1/2, 1) U (2, ∞) - {\(\frac{3+\sqrt5}2,\frac{3-\sqrt5}2\)}