Find the domain of the function.

Question

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.