NTA Abhyas JEE Main2020MathematicsFunctionsPractice

The domain of f x = x 16 - x 2 + l o g 2 x 3 - 2 x is

Options

A- 2 , 0 ∪ 2 , ∞
B- 2 , 0 ∪ 2 , 4
C- 2 , 0 ∪ 4 , ∞
D- 2 , 0 ∪ 2 , 4 ∪ 4 , ∞

Correct answer

D. - 2 , 0 ∪ 2 , 4 ∪ 4 , ∞

Step-by-step solution

16 - x 2 ≠ 0 and x 3 - 2 x > 0 x ≠ 4 , - 4     … . . i and x x 2 - 2 > 0 x x + 2 x - 2 > 0 x ∈ - 2 , 0 ∪ 2 , ∞ … i i Taking intersection of i   &   i i , we get, x ∈ - 2 , 0 ∪ 2 , 4 ∪ 4 , ∞

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