Question

The domain of the function f(x) = √(sin^-1(log₃x))+ tan^-1x/√(x²-5x+6) is-

(A) [1, 3] 

(B) [1, 3) 

(C) [1, 2) ⋃ (2, 3] 

(D) [1, 2)

Answer 1

sin–1 (log₃ x) ≥ 0 

⇒ 0 ≤ log₃ x ≤ 1 

⇒ 1 ≤ x ≤ 3 ......(i)

for tan^–1x, x ∈ R .....(ii)

For √(x-5x+ 6), x² – 5x + 6 > 0

∴ (x – 2) (x – 3) > 0

(–∞, 2) ⋃ (3, ∞) ......(iii) 

(i) ⋂ (ii) ⋂ (iii) 

∴ D_f = [1, 2)