Q37 / 87 · NTA Abhyas (JEE Main) 2020 · Mathematics · Functions

The domain of the function $f (x) = \log_{3} [1 - \log_{6} (x^{2} - 7 x + 16)]$ is

Solution

f (x)

is defined if

1 - {log}_{6} (x^{2} - 7 x + 16) > 0

and

x^{2} - 7 x + 16 > 0

\Rightarrow {log}_{6} (x^{2} - 7 x + 16) < 1

and

{(x - \frac{7}{2})}^{2} + \frac{15}{4} > 0

\Rightarrow x^{2} - 7 x + 16 < 6

[∵ {(x - \frac{7}{2})}^{2} + \frac{15}{4} > 0 f o r a l l r e a l x]

\Rightarrow x^{2} - 7 x + 10 < 0

\Rightarrow (x - 2) (x - 5) < 0 \Rightarrow 2 < x < 5

∴

Domain of

f = (2, 5)

Hence, the correct answer is option: 'A'.