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0 votes
19.7k views
in Sets, relations and functions by (53.1k points)

The domain of the function f(x) = log3+x (X2 - 1) is

(A) (-3,-1) ∪ (1,∞) 

(B) (-3,-1) ∪ (1,∞) 

(C) (-3,-2) ∪ (-2,-1) ∪(1,∞)

(D)  (-3,-2) ∪ (-2,-1)∪(1,∞)

1 Answer

+1 vote
by (53.3k points)
selected by
 
Best answer

Correct option  (B) (-3,-1) ∪ (1,∞) 

Explanation :

The function f(x) is to be defined when x2 − 1>0. So,

x2 > 1,⇒ x< -1 or X > 1 and 3 + x > 0

Therefore, x > −3 and x ≠ −2 and hence,

Df = (− 3 − 2)∪ (− 2, -1)∪ (1,∞)

by (10 points)
Why x should not be equal to -2??
by (24.8k points)
Given function is f(x) = log_(3+x) (x^2-1) ⟹ x^2-1 = (3+x)^f(x), then at x = -2, L.H.S. = 4-1 = 3 but R.H.S. = (-2+1)^f(x) = 1^f(x) =1. Hence, L.H.S. ≠ R.H.S. Thus, given function is not defined at x = -2

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