Question 253169: If x is between 0 and 1, which of the following increases as x increases ?
I. 1 - x^2
II. x – 1
III. 1/x^2
(A) I and II (B) II and III (C) I and III (D) II only (E) I only
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! If x is between 0 and 1, which of the following increases as x increases ?
I. 1 - x^2
II. x – 1
III. 1/x^2
One way to solve this is put in numbers: 0, 1/2, 1. Let's look at each, one at a time.
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I. 1 - X^2:
x = 0, we get 1
x = 1/2, we get 3/4
x = 1, we get 0. Clearly not increasing.
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II. x - 1
x = 0, we get -1
x = 1/2, we get - 1/2
x = 1, we get 0. Clearly increasing.
--
III. 1 / X^2:
x = 0, we get undefined.
x = 1/2, we get 4
x = 1, we get 1. Clearly not increasing.
So, our answer is [D]
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