XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

XAT Previous Year Paper | XAT QADI Questions | Question 23

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Question 23 : Consider the real-valued function .

Find the domain of f(x).

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Explanatory Answer

Given that, f(x) = \(\frac{\log (3 x-7)}{\sqrt{2 x^{2}-7 x+6}}\)
The log values should always be positive. So 3x - 7 > 0
=> 3x > 7
Or, x > \(\frac{7}{3}\)
The value in the root should always be positive and the value in the denominator should not be equal to zero.
\(2 x^{2}-7 x+6\) > 0
(x - 2)(2x - 3) > 0
x < 2 and x > \(\frac{3}{2}\)
Hence we have x > \(\frac{7}{3}\),x < 2 and x > \(\frac{3}{2}\)
Therefore we can say that x should be always greater than \(\frac{7}{3}\)
It is represented by (\(\frac{7}{3}\),∞)

The question is " Consider the real-valued function .

Find the domain of f(x). "

Hence, the answer is ''

Choice C is the correct answer.

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