## Chapter 3.2

## Q. 3.2.10

## Q. 3.2.10

** Finding Domains of Natural Logarithmic Functions**

Find the domain of each function:

**a. **f(x) = ln(3 – x) **b. **h(x) = ln(x – 3)².

## Step-by-Step

## Verified Solution

**a.** The domain of f consists of all x for which 3 – x > 0. Solving this inequality for x, we obtain x < 3. Thus, the domain of f is \{x \mid x<3\} or (-∞, 3). This is verified by the graph in **Figure 3.14.**

**b.** The domain of h consists of all x for which (x-3)^2>0. It follows that the domain of h is all real numbers except 3 . Thus, the domain of h is \{x \mid x \neq 3\} or (-∞, 3) \cup(3, \infty). This is shown by the graph in **Figure 3.15**. To make it more obvious that 3 is excluded from the domain, we used a DOT format.