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Inequalities - Quant/Math - CAT 2009
Question 4 the day:
July 11, 2003
The question for the day is from the topic of Inequalities.
- For what values of 'x' will the function
 be defined in the real domain?
| (1) |
-10 < x < 4 |
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(2) |
–4 < x < 10 |
| (3) |
x does not lie between the closed interval –10 and 4 |
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(4) |
x does not lie between the open interval –4 and 10 |
Correct Answer - (4)
Solution:
The function is defined in the real domain only when x2 – 6x – 40 > 0.
When x2 – 6x – 40 is < 0, the function will be imaginary.
Now let us find out the range of values for which x2 – 6x – 40 > 0.
Factorizing, we get (x – 10)(x + 4) > 0
This value of (x – 10)(x + 4) will be greater than or equal to 0 when both (x – 10) and (x + 4) are greater than or equal to 0 or when both (x - 10) and (x + 4) are less than or equal 0.
Case 1: When both (x – 10) and (x + 4) are greater than or equal to 0.
X > 10 and x > - 4 => when x > 10 it will be greater than –4.
Therefore it will suffice to say that x > 10
Case 2: When both (x - 10) and (x + 4) are less than or equal to 0.
i.e. x < 10 and x < -4 => when x < -4, it will less than 10.
Therefore, it will suffice to say that x < -4
Hence, the range in which the given function will be defined in the real domain will be when x does not lie between –4 and 10.
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