Question

find the domain of f(x).
$f(x) = \frac{3x - 6}{6x + 6}$

Explanation:

Step1: Identify the restriction

For a rational function \( f(x)=\frac{3x - 6}{6x + 6} \), the denominator cannot be zero. So we set the denominator equal to zero and solve for \( x \):
\( 6x + 6 = 0 \)

Step2: Solve the equation

Subtract 6 from both sides: \( 6x = -6 \)
Divide both sides by 6: \( x = -1 \)

Step3: Determine the domain

The domain of a function is all real numbers except the values that make the denominator zero. So the domain of \( f(x) \) is all real numbers except \( x = -1 \).

Answer:

The domain of \( f(x) \) is all real numbers \( x \) such that \( x
eq -1 \), or in interval notation, \( (-\infty, -1) \cup (-1, \infty) \).