NTA Abhyas JEE Main2020MathematicsFunctionsPractice

The domain of the function f x = l o g 2 1 - l o g 12 x 2 - 5 x + 16 is

Options

A1,4
B- ∞ , 4
C1 , ∞
D1,4

Correct answer

A. 1,4

Step-by-step solution

The function f x is defined if 1 - l o g 12 x 2 - 5 x + 16 > 0 and x 2 - 5 x + 16 > 0 ⇒ l o g 12 x 2 - 5 x + 16 < 1 and x - 5 2 2 + 39 4 > 0 ⇒ x 2 - 5 x + 16 < 12 ∵ x - 5 2 2 + 39 4 > 0 ,   ∀ x ∈ R ⇒ x 2 - 5 x + 4 < 0 ⇒ x - 1 x - 4 < 0 ⇒ 1 < x < 4 ∴ Domain of f = 1,4

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