Which statement describes the domain of the function f(x) = 3x / 4x2-4 ?A. all real numbersB. all nonzero real numbersC. all real numbers except x = 3/4D. all real numbers except x = –1 and x = 1

Given rational function: [tex]f(x)=\frac{3x}{4x^2-4}[/tex].We need to find the domain of the given rational function.In order to find the domain, we need to find the restrictions of the domain.In order to find the restrictions, we need to set denominator equal to 0 and solve for x.Therefore, [tex]4x^2-4 =0[/tex]Adding 4 on both sides, we get [tex]4x^2+4 -4 = 0+4[/tex][tex]4x^2 = 4.[/tex]Dividing both sides by 4, we get [tex]\frac{4x^2}{4} = \frac{4}{4}[/tex][tex]x^2=1[/tex]Taking square root on both sides, we get [tex]\sqrt{x^2} =\sqrt{1}[/tex]x = +1, =-1.Therefore, domain is all real numbers except x = –1 and x = 1.So, the correct option is D. all real numbers except x = –1 and x = 1.