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Chapter 2: Problem 54

Find the domain of each function. $$g(x)=\frac{2}{x+5}$$

Short Answer

Expert verified
The domain of the function \( g(x) = \frac{2}{x+5} \) is \( x \in \mathbb{R}, x \neq -5 \), or in interval notation, \( (-\infty, -5) \cup (-5, +\infty) \).

Step by step solution

01

Identify the function

The given function is \( g(x) = \frac{2}{x+5} \). We want to find the values for x that are permissible.
02

Determine when the denominator equals zero

For the function \( g(x) = \frac{2}{x+5} \), the denominator of the fraction cannot be equal to zero since division by zero is undefined. Therefore, we shall find the value of x for which the denominator \( x + 5 = 0 \). So, \( x = -5 \).
03

Determine the domain of the function

Every real number is permitted, except for \(x = -5\), which would make the denominator of the function equal to zero. Hence, the domain of the function \( g(x) = \frac{2}{x+5} \) is \( x \in \mathbb{R}, x \neq -5 \), or in interval notation, \( (-\infty, -5) \cup (-5, +\infty) \).

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