SOLUTION: If the value of x lies between 0 & 1 which of the following is the largest? (a) x b) x2 (c) -x (d) 1/x

Question 262687: If the value of x lies between 0 & 1 which of the following is the largest?
(a) x b) x2 (c) -x (d) 1/x

Found 2 solutions by CubeyThePenguin, greenestamps:
Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website!
Assume x = 1/2.

A = x = 1/2
B = x^2 = 1/4
C = -x = -1/2
D = 1/x = 2

The largest is D.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Another response from tutor @CubeyThePenguin written hastily and carelessly, and showing bad mathematics.

You can't answer the question by choosing one number between 0 and 1 and evaluating the four expressions for that one number.

To find the answer using correct mathematical procedures, you need to analyze each of the given expressions. Specifically, you need to compare answer choices b, c, and d to answer choice a -- i.e., you need to compare each of expressions b, c, and d to the input value (a) when that input value is between 0 and 1.

Answer choice b squares the input value x. Squaring a number between 0 and 1 results in a number smaller than you started with. So for x between 0 and 1, x^2 is less than x. So answer choice b is not right.

Obviously answer choice c is not right; the opposite of a number between 0 and 1 is negative, so choice c gives you a number less than what you started with.

Answer choice d takes the reciprocal of the input number; that is, it divides 1 by the input number.

Dividing 1 by a number between 0 and 1 gives a positive number greater than 1. So if x is between 0 and 1, 1/x is always greater than x. So answer choice d is the correct answer.

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