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# For which of the following functions is f(-1/2) > f(2)?

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Joined: 02 Sep 2009
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For which of the following functions is f(-1/2) > f(2)?  [#permalink]

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04 Mar 2019, 00:31
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For which of the following functions is f(-1/2) > f(2)?

A. f(x) = 3*x^2

B. f(x) = 3*x

C. f(x) = 3 + x^2

D. f(x) = 3 + 1/x

E. f(x) = 3/x^2

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Re: For which of the following functions is f(-1/2) > f(2)?  [#permalink]

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04 Mar 2019, 00:48
E.

Just put the values of -1/2 and 2.

A faster way could be to see where x is negative or in denominator. That would increase the value of -1/2 and reduce the value of 2.

In E. 3/(-1/2)^2 = 12
And 3/(2^2) = 3/4 =0.75

12>0.75

So E

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Re: For which of the following functions is f(-1/2) > f(2)?  [#permalink]

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04 Mar 2019, 01:15
Bunuel wrote:
For which of the following functions is f(-1/2) > f(2)?

A. f(x) = 3*x^2

B. f(x) = 3*x

C. f(x) = 3 + x^2

D. f(x) = 3 + 1/x

E. f(x) = 3/x^2

only for f(x) = 3/x^2
we get f(-1/2) > f(2)
IMO E
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Joined: 21 Apr 2014
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Re: For which of the following functions is f(-1/2) > f(2)?  [#permalink]

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04 Mar 2019, 02:02
1
Students get confused on these type of questions sometimes because we aren't generally used to plugging into answer choices TWICE. But that's what you have to do for each answer choice. You have to plug in -1/2 and then also plug in 2, and see is the result when you plug in -1/2 is greater than the result when you plug in 2. This will only be true for ONE answer choice.

A. f(x) = 3*x^2

If x = -1/2, then f(x) = 3/4.
If x = 2, then f(x) = 12.

Is 3/4 > 12? Nope! Cross this one off.

B. f(x) = 3*x

If x = -1/2, then f(x) = -3/4.
If x = 2, then f(x) = 6.

Is -3/4 > 6? Nope!

C. f(x) = 3 + x^2

If x = -1/2, then f(x) = 3.25
If x = 2, then f(x) = 7

Is 3.25 > 7? No!

D. f(x) = 3 + 1/x

If x = -1/2, then f(x) = -2
If x = 2, then f(x) = 3.5

Is -1/2 > 3.5? Nope.

E. f(x) = 3/x^2

If x = -1/2, then f(x) = 12
If x = 2, then f(x) = 3/4

Is 12 > 3/4? Yes! We finally have an answer!

Even though it's a PS question, it kind of has that Data Sufficiency vibe in which you're testing cases. Here we had to "test out" each of the answer choices and see which one gave us the relationship we were looking for.
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Re: For which of the following functions is f(-1/2) > f(2)?  [#permalink]

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06 Mar 2019, 20:16
Bunuel wrote:
For which of the following functions is f(-1/2) > f(2)?

A. f(x) = 3*x^2

B. f(x) = 3*x

C. f(x) = 3 + x^2

D. f(x) = 3 + 1/x

E. f(x) = 3/x^2

Starting with E, we have:

f(-1/2) = 3/(-1/2)^2 = 3/(1/4) = 12

f(2) = 3/(2^2) = 3/4

We see that f(-1/2) > f(2), so answer is E correct.

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Re: For which of the following functions is f(-1/2) > f(2)?   [#permalink] 06 Mar 2019, 20:16
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# For which of the following functions is f(-1/2) > f(2)?

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