NTA Abhyas JEE Main2020MathematicsFunctionsPractice

The domain of the function f x = log 3 ⁡ 1 - log 6 ⁡ x 2 - 7 x + 16 is

Options

A2 , 5
B∞ , 5
C2 , ∞
D2 , 5

Correct answer

A. 2 , 5

Step-by-step solution

f x is defined if 1 - log 6 ⁡ x 2 - 7 x + 16 > 0 and x 2 - 7 x + 16 > 0 ⇒ log 6 ⁡ x 2 - 7 x + 16 < 1 and x - 7 2 2 + 15 4 > 0 ⇒ x 2 - 7 x + 16 < 6 ∵ x - 7 2 2 + 15 4 > 0  f o r  a l l  r e a l  x ⇒ x 2 - 7 x + 10 < 0 ⇒ x - 2 x - 5 < 0 ⇒ 2 < x < 5 ∴ Domain of f = 2 , 5

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