Question

Find the domain of the function.
yequalsnegative 5plusStartFraction 8 Over 4 x plus 8 EndFraction
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Part 1
A.
​(minusinfinity​, negative 2​)
B.
All real numbers except 2
C.
All real numbers except negative 2
D.
​(negative 2​, infinity​)

Answer 1

To find the domain of the function given by

\[
y = -5 + \frac{8}{4x + 8},
\]

we need to determine the values of \( x \) for which the function is defined. The only restriction comes from the denominator of the fraction, since division by zero is undefined.

1. **Set the denominator equal to zero and solve for \( x \)**:
\[
4x + 8 = 0
\]
\[
4x = -8
\]
\[
x = -2
\]

2. **Identify the restrictions**:
The function is undefined when \( x = -2 \).

3. **State the domain**:
The domain includes all real numbers except \( -2 \).

Thus, the domain of the function is:

\[
\text{All real numbers except } -2.
\]

This corresponds to option **C. All real numbers except negative 2**.