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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8149
GMAT 1: 760 Q51 V42 GPA: 3.82
The function f is defined by f(x) = - k/x^2 for all nonzero numbers x  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 66% (01:13) correct 34% (01:05) wrong based on 120 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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Math Expert V
Joined: 02 Aug 2009
Posts: 8183
Re: The function f is defined by f(x) = - k/x^2 for all nonzero numbers x  [#permalink]

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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
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8149
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]

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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

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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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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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Target Test Prep Representative G
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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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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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_________________ Re: The function f is defined by f(x) = - k/x^2 for all nonzero numbers x   [#permalink] 15 Oct 2018, 18:30
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