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a function is shown: f(x) = 4x2 − 1.

choose the equivalent function that best shows the x-intercepts on the graph.

f(x) = (4x + 1)(4x − 1)

f(x) = (2x + 1)(2x − 1)

f(x) = 4(x2 + 1)

f(x) = 2(x2 − 1)

f(x) = (2x + 1)(2x − 1)

Explanation:

As we can see from the above function f(x) = 4 − 1, we need to find x-intercept, i.e., the value of x where this function's value is zero.

So let us Equate the function with zero

4 - 1 = 0 => 4 = 1 => = 1/4 => x =

Hence we get 2 values of x, i.e., +1/2, and -1/2.

So now we need to check out the functions which are zero at this values of x, so let us substitute values of x in each and every option and see the values of functions.

Option A - f(x) = (4x + 1)(4x − 1) = 3, -3

Option B - f(x) = (2x + 1)(2x − 1)  = 0

Option C - f(x) = 4(x2 + 1)  = 5

Option D - f(x) = 2(x2 − 1) = -3/2

Hence answer is Option B

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step-by-step explanation: