Questions: Part 2 of 3 (b) y(x) = x / (x+1+4) The domain in interval notation is .

Solution Steps

To determine the domain of the function \( y(x) = \frac{x}{|x+1|+4} \), we need to identify the values of \( x \) for which the function is defined. The function is defined for all real numbers \( x \) because the denominator \( |x+1| + 4 \) is always positive and never zero.

The given function is \( y(x) = \frac{x}{|x+1| + 4} \).

The denominator of the function is \( |x+1| + 4 \). Since the absolute value function \( |x+1| \) is always non-negative, and adding 4 ensures that the denominator is always positive and never zero.

Since the denominator \( |x+1| + 4 \) is always positive for all real numbers \( x \), the function \( y(x) \) is defined for all real numbers.

Final Answer