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The problem definition is funny. Is it supposed to be (-x)^2 or -(x^2) as the term in the problem? If it is -(x^2) which is how I read it, the bold part in the answer above is wrong and 2 is correct. Otherwise the above solution is correct.Anonymous wrote:If X is a positive integer, then x and x^2 should always be greater than or equal to 1 and 2x is always greater than or equal to 2. Having said that, 1/x is less than or equal to 1 because 1/1 is 1 and as x gets larger, 1/x becomes smaller.
Having said that, any answer choice that places 2x to the left of 1/x can be eliminated because the minimum value for 2x is 2, and the maximum value for 1/x is 1, so 2x must always be greater than 1/x. You can eliminate 1 & 3.
Now, with #2: can x^2 be smaller than 1/x? x^2 can be equal to 1/x, but it can never be smaller. Again, when x=1 both x^2 and 1/x also equal to 1. However, as x gets larger, the value of x^2 gets larger while the value of 1/x gets smaller. So 2 is also out because it says that x^2 could be larger than 1/x which is not true.
