1. **State the problem:** We are given two functions as sets of ordered pairs: $f = \{(-3,0),(1,-1)\}$ and $g = \{(-3,-5),(4,1),(5,6)\}$. We need to find the composition $f \circ g$ and its domain. 2. **Recall the definition of composition:** The composition $f \circ g$ means $f(g(x))$. For each $x$ in the domain of $g$, we find $g(x)$, then apply $f$ to that result. 3. **Find $f \circ g$: ** - For $x = -3$, $g(-3) = -5$. Check if $-5$ is in the domain of $f$ (the first elements of $f$ are $-3$ and $1$). It is not, so $f(g(-3))$ is undefined. - For $x = 4$, $g(4) = 1$. Check if $1$ is in the domain of $f$. Yes, $f(1) = -1$. So $f(g(4)) = -1$. - For $x = 5$, $g(5) = 6$. Check if $6$ is in the domain of $f$. No, so $f(g(5))$ is undefined. 4. **Write the composition set:** $$f \circ g = \{(4, -1)\}$$ 5. **Find the domain of $f \circ g$: ** The domain consists of all $x$ values in the domain of $g$ for which $g(x)$ is in the domain of $f$. Only $x=4$ satisfies this. **Final answer:** $$f \circ g = \{(4, -1)\}$$ $$\text{Domain} = \{4\}$$