Problem 60 - Algebra and Trigonometry Real Mathematics, Real People

Question

Find the domain of the function. $$s(y)=\frac{3 y}{y+5}$$

Step-by-Step Solution

Answer

The domain of the function \(s(y)=\frac{3 y}{y+5}\) is \(y \neq -5\) or in interval notation: \(y \in (-\infty, -5) \cup (-5, +\infty)\).

Step 1: Identify the Denominator

The denominator of the function given is \(y + 5\).

Step 2: Equate the denominator to zero and solve for y

Solve \(y + 5 = 0\) to find the 'y' value that makes the denominator zero. Solving for 'y' gives \(y = -5\).

Step 3: Define the domain based on step 2

The function is undefined for \(y = -5\), therefore, the domain does not include -5. Hence the domain of the function \(s(y)=\frac{3 y}{y+5}\) is \(y \neq -5\), or in interval notation: \(y \in (-\infty, -5) \cup (-5, +\infty)\).