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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