which statement describes the domain of the function $f(x)=\frac{3x}{4x^{2}-4}$?\no all real numbers\no all…

which statement describes the domain of the function $f(x)=\frac{3x}{4x^{2}-4}$?\no all real numbers\no all nonzero real numbers\no all real numbers except $x = \frac{3}{4}$\no all real numbers except $x=-1$ and $x = 1$

which statement describes the domain of the function $f(x)=\frac{3x}{4x^{2}-4}$?\no all real numbers\no all nonzero real numbers\no all real numbers except $x = \frac{3}{4}$\no all real numbers except $x=-1$ and $x = 1$

Answer

Answer:

D. all real numbers except (x = - 1) and (x = 1)

Explanation:

Step1: Recall domain - definition

The domain of a rational function is all real numbers except where the denominator is zero.

Step2: Set denominator equal to zero

Set (4x^{2}-4 = 0).

Step3: Factor the equation

Factor out 4: (4(x^{2}-1)=0), then use difference - of - squares (a^{2}-b^{2}=(a + b)(a - b)) to get (4(x + 1)(x - 1)=0).

Step4: Solve for (x)

Set each factor equal to zero: (x+1 = 0) gives (x=-1), and (x - 1=0) gives (x = 1). So the domain is all real numbers except (x=-1) and (x = 1).