The domain of the function fx=x+1 x-3x-2is (a) [ 1, 2) ∪ [3, ) (b) ( 1, 2) ∪ - Maths -

Question

The domain of the function f x = x + 1   x - 3 x - 2 is
(a) [−1, 2) ∪ [3, ∞)
(b) (−1, 2) ∪ [3, ∞)
(c) [−1, 2] ∪ [3, ∞)
(d) None of these

Global Expert · Accepted Answer

(a) [−1, 2) ∪ [3, ∞)

fx=x+1 x-3x-2
For f(x) to be defined,(x-2) ≠0⇒x ≠ 2           
(1)Also,(x+1)(x-3)(x-2)≥0⇒(x+1)(x-3)(x-2)(x-2)2≥0⇒(x+1)(x-3)(x-2)≥0⇒x ∈ [-1,2)∪[3,∞)   
(2)From (1) and (2),x ∈ [-1,2) ∪ [3,∞)

The domain of the function f x = x + 1 x - 3 x - 2 is (a) [−1, 2) ∪ [3, ∞) (b) (−1, 2) ∪ [3, ∞) (c) [−1, 2] ∪ [3, ∞) (d) None of these

The domain of the function $f (x) = \sqrt{\frac{(x + 1) (x - 3)}{x - 2}}$ is
(a) [−1, 2) ∪ [3, ∞)
(b) (−1, 2) ∪ [3, ∞)
(c) [−1, 2] ∪ [3, ∞)
(d) None of these