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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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New post 03 Jan 2017, 17:33
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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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Re: The function f is defined by f(x) = - k/x^2 for all nonzero numbers x  [#permalink]

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New post 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
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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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New post 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
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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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New post 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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New post 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

Answer: A
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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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New post 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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