From: JEE Main 2019 (Online) 9th April Evening Slot
Question
The domain of the definition of the function
f(x)=4−x21+log10(x3−x) is
Choose an option
▸Show full solutionCorrect option: A
Correct answer
A(-1, 0) ∪ (1, 2) ∪ (2, ∞)
Step-by-step explanation
Given f(x)=4−x21+log10(x3−x)
Let f1(x) = 4−x21 and f2(x) = log10(x3−x)
Here in f1(x) denominator = 0
4 - x2= 0
⇒ x =± 2 ...........(1)
and x3 - x > 0
⇒ x(x2 - 1) > 0
⇒ x(x + 1)(x - 1) > 0
x ∈ (-1, 0) ∪ (1, ∞) ........(2)
Hence domain is intersection of (1) and (2)
x ∈ (-1, 0) ∪ (1, 2) ∪ (2, ∞)
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