Answer:
f(x) = (2x + 1)(2x − 1)
Explanation:
As we can see from the above function f(x) = 4[tex]x^{2}[/tex] − 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[tex]x^{2}[/tex] - 1 = 0 => 4[tex]x^{2}[/tex] = 1 => [tex]x^{2}[/tex] = 1/4 => x = [tex]\sqrt{1/4}[/tex]
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
