Question

find the domain of f(x).
$f(x) = \frac{2x + 9}{4x + 4}$
answer attempt 1 out of 2
answer type: interval
interval:

Explanation:

Step1: Identify the restriction

For a rational function \( f(x)=\frac{2x + 9}{4x+4} \), the denominator cannot be zero. So we set the denominator equal to zero and solve for \( x \):
\( 4x + 4=0 \)

Step2: Solve for \( x \)

Subtract 4 from both sides: \( 4x=- 4 \)
Divide both sides by 4: \( x = - 1 \)

Step3: Determine the domain

The domain is all real numbers except \( x=-1 \). In interval notation, this is \( (-\infty,-1)\cup(-1,\infty) \)

Answer:

\( (-\infty, -1) \cup (-1, \infty) \)