x এর মান 2 থেকে হ্রাস পেয়ে -2 হলে, নিচের কোনটি অবশ্যই বৃদ্ধি পাবে?
Let's analyze each option:
A) 1/x - 3:
When x decreases from 2 to -2, 1/x - 3 will definitely increase. When x is 2, 1/x - 3 is 1/2 - 3 = -2.5. When x is -2, 1/x - 3 is 1/(-2) - 3 = -0.5 - 3 = -3.5. So, as x decreases from 2 to -2, the value of 1/x - 3 increases.
B) 1 + 1/x:
When x decreases from 2 to -2, 1 + 1/x will not definitely increase. When x is 2, 1 + 1/x is 1 + 1/2 = 1.5. When x is -2, 1 + 1/x is 1 + 1/(-2) = 1 - 0.5 = 0.5. So, as x decreases from 2 to -2, the value of 1 + 1/x does not always increase.
C) 5 - (x * x):
When x decreases from 2 to -2, 5 - (x * x) will not definitely increase. When x is 2, 5 - (x * x) is 5 - (2 * 2) = 5 - 4 = 1. When x is -2, 5 - (x * x) is 5 - ((-2) * (-2)) = 5 - 4 = 1. So, as x decreases from 2 to -2, the value of 5 - (x * x) does not always increase.
D) 2 + x:
When x decreases from 2 to -2, 2 + x will not definitely increase. When x is 2, 2 + x is 2 + 2 = 4. When x is -2, 2 + x is 2 - 2 = 0. So, as x decreases from 2 to -2, the value of 2 + x does not always increase.
Therefore, the option A) 1/x - 3 is the correct choice because as x decreases from 2 to -2, the value of 1/x - 3 definitely increases.
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