Exploring the Domain: When is (49+2x)/(x+4) Defined?

To determine the domain of the function $\frac{49 + 2x}{x + 4}$, we need to focus on avoiding division by zero, which occurs when the denominator is zero.

Let's identify the denominator of the function:

• The denominator is $x + 4$.

Next, we set the denominator equal to zero and solve for $x$:

• $x + 4 = 0$
• Subtract 4 from both sides: $x = -4$

This calculation shows that the function is undefined when $x = -4$. Thus, the domain of the function is all real numbers except $x = -4$.

Therefore, the domain of the function is $x \neq -4$.

In terms of the provided choices, this corresponds to choice 4:

Yes, $x \ne -4$