Question

1. find the domain of the function: $g(w) = \frac{5w}{w - 1}$

a) $w = 1$ d) $(-\infty, 1) \cup (1, \infty)$
b) $(-\infty, 0) \cup (0, 1) \cup (1, \infty)$ e) $(-\infty, \infty)$
c) $w = 1, w = 0$

Explanation:

Step1: Identify the restriction

For a rational function \( g(w)=\frac{5w}{w - 1} \), the denominator cannot be zero. So we set \( w-1
eq0 \).

Step2: Solve the inequality

Solving \( w - 1
eq0 \) gives \( w
eq1 \). This means the domain includes all real numbers except \( w = 1 \). In interval notation, this is \( (-\infty,1)\cup(1,\infty) \).

Answer:

d) \((-\infty, 1)\cup(1, \infty)\)