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# The function f is defined by f(x) = - k/x^2 for all nonzero numbers x

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The function f is defined by f(x) = - k/x^2 for all nonzero numbers x  [#permalink]

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03 Jan 2017, 17:33
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35% (medium)

Question Stats:

69% (01:13) correct 31% (01:00) wrong based on 102 sessions

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The function f is defined by $$f(x) = - k/x^2$$ for all nonzero numbers x (k is constant). If f(2) = 1/4, then f(1/2) =?

A) 4

B) 1/4

C) - 1/4

D) -4

E) -2

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7334 Re: The function f is defined by f(x) = - k/x^2 for all nonzero numbers x [#permalink] ### Show Tags 04 Jan 2017, 17:30 1 MathRevolution wrote: The function f is defined by $$f(x) = - k/x^2$$ for all nonzero numbers x (k is constant). If f(2) = 1/4, then f(1/2) =? A) 4 B) 1/4 C) - 1/4 D) -4 E) -2 Hi F(x)=-k/x^2, so F(2)=-k/2^2=-k/4 but F(2) is given as 1/4 So F(2)=-k/4=1/4 or k=-1.... Now we can find any function as constant'k' is known.. F(1/2) =-(-1)/(1/2)^2=1/(1/4)=4.. A _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html GMAT Expert Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6949 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The function f is defined by f(x) = - k/x^2 for all nonzero numbers x [#permalink] ### Show Tags 05 Jan 2017, 04:43 If f(x)=-k/x2, f(2)=-k/22=-k/4=1/4, then k=-1. If so, f(x)=-(-1)/x2=1/x2, then f(1/2)=1/(1/2)2=4 The answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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The function f is defined by f(x) = - k/x^2 for all nonzero numbers x  [#permalink]

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05 Jan 2017, 08:43
MathRevolution wrote:
The function f is defined by $$f(x) = - k/x^2$$ for all nonzero numbers x (k is constant). If f(2) = 1/4, then f(1/2) =?

A) 4

B) 1/4

C) - 1/4

D) -4

E) -2

Since, $$f(x) = - \frac{k}{x^2}$$ & $$f(2) = \frac{1}{4}$$

So, $$k = 1$$ & $$x =$$ + $$2$$

Now, $$f(\frac{1}{2}) = 1/\frac{1}{4}$$

Hence, $$f(\frac{1}{2}) = 4$$

Thus, answer will be (A) 4
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Re: The function f is defined by f(x) = - k/x^2 for all nonzero numbers x  [#permalink]

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06 Jan 2017, 10:14
MathRevolution wrote:
The function f is defined by $$f(x) = - k/x^2$$ for all nonzero numbers x (k is constant). If f(2) = 1/4, then f(1/2) =?

A) 4

B) 1/4

C) - 1/4

D) -4

E) -2

We are given the following function:

f(x) = -k/(x^2)

We need to determine the value of k. Since f(2) = 1/4, we substitute 2 for x and 1/4 for f(2) in the given equation:

-k/(2^2) = 1/4

-k/4 = 1/4

k = -1

Now we can determine f(1/2):

-(-1)/(1/2)^2 = 1/(1/4) = 4

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Re: The function f is defined by f(x) = - k/x^2 for all nonzero numbers x  [#permalink]

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15 Oct 2018, 17:30
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Re: The function f is defined by f(x) = - k/x^2 for all nonzero numbers x   [#permalink] 15 Oct 2018, 17:30
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