Question

1. the graphs of the functions f and g are shown below. use these graphs to find each of the following. (a) (f + g)(2) (b) the domain of (f/g)(x)

Explanation:

Step1: Recall domain - function rule

The domain of $\frac{f}{g}(x)$ is the set of all $x$ - values that are in the domain of both $f(x)$ and $g(x)$ and for which $g(x)
eq0$.

Step2: Analyze domain from graphs

First, find the domain of $f(x)$ and $g(x)$ from the graphs. Then, exclude the $x$ - values for which $g(x) = 0$.

Step3: Determine domain intervals

From the graphs, identify the intervals of $x$ that satisfy the above - mentioned conditions.

Answer:

The domain of $\frac{f}{g}(x)$ needs to be determined by observing the $x$ - values where both $f(x)$ and $g(x)$ are defined and $g(x)
eq0$ from the given graphs. Without the actual numerical values of the endpoints of the intervals on the graphs, we can't give a specific numerical answer, but the general process is as described above. If we assume the domain of $f(x)$ is $[a,b]$ and the domain of $g(x)$ is $[c,d]$ and $g(x)$ has zeros at $x = e$ and $x = f$ (where $e,f\in[c,d]$), then the domain of $\frac{f}{g}(x)$ is $([a,b]\cap[c,d])\setminus\{e,f\}$.