Question

which statement describes the domain of the function $f(x)=\frac{3x}{4x^2 - 4}$?

• all real numbers
• all nonzero real numbers
• all real numbers except $x = \frac{3}{4}$
• all real numbers except $x = -1$ and $x = 1$

Explanation:

Step1: Set denominator equal to 0

$4x^2 - 4 = 0$

Step2: Solve for $x$

Factor: $4(x^2 - 1) = 0$
$x^2 - 1 = 0$
$x^2 = 1$
$x = \pm 1$

Step3: Identify domain restrictions

The function is undefined when $x=1$ or $x=-1$, so the domain excludes these values.

Answer:

all real numbers except $x = -1$ and $x = 1$