x 2 − 1 > 0 ⇒ x 2 > 1 x>1" class="fm-inline"> ⇒ − 1 > x > 1 , and 0" class="fm-inline"> 3 + x > 0 ⇒ − 3 < x and x ≠ − 2 ∴ domain of the function is D f = ( − 3 , − 2 ) ∪ ( − 2 , − 1 ) ∪ ( 1 , ∞ )" >
Given that, f(x)=log3+x(x2−1) The given function is defined when x2−1 is greater than zero i.e., x2−1>0⇒x2>1 ⇒−1>x>1, and 3+x>0 ⇒−3<x and x≠−2 ∴ domain of the function is Df=(−3,−2)∪(−2,−1)∪(1,∞)
