NTA Abhyas JEE Main2020MathematicsFunctionsPractice

The domain of the function f x = 1 x 2 - x - 20 is (where, . represents the greatest integer function)

Options

A- ∞ , - 4 ∪ [ 6 , ∞ )
B( - ∞ , 4 ] ∪ [ 6 , ∞ )
C- ∞ , - 4 ∪ ( 6 , ∞ )
DNone of these

Correct answer

A. - ∞ , - 4 ∪ [ 6 , ∞ )

Step-by-step solution

f x is defined for x 2 - x - 20 > 0 ⇒ x - 5 x + 4 > 0 ⇒ x < - 4 or x > 5 But x < - 4 ⇒ x = - 5 , - 6 , - 7 … ∴ x < - 4 Also, x > 5 ⇒ x = 6 , 7 , 8 … ∴ x ≥ 6 ∴ Domain of f = - ∞ , - 4 ∪ [ 6 , ∞ )

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