1. **State the problem:** We are given two functions $f(x) = x + 4$ and $g(x) = 2x + 3$. We need to find the composite functions $(f \circ g)(x)$, $(g \circ f)(x)$, and then evaluate these composites at $x = -2$. 2. **Recall the definition of composite functions:** - $(f \circ g)(x) = f(g(x))$ means we substitute $g(x)$ into $f$. - $(g \circ f)(x) = g(f(x))$ means we substitute $f(x)$ into $g$. 3. **Find $(f \circ g)(x)$:** - Start with $g(x) = 2x + 3$. - Substitute into $f$: $f(g(x)) = f(2x + 3) = (2x + 3) + 4$. - Simplify: $2x + 3 + 4 = 2x + 7$. 4. **Find $(g \circ f)(x)$:** - Start with $f(x) = x + 4$. - Substitute into $g$: $g(f(x)) = g(x + 4) = 2(x + 4) + 3$. - Simplify: $2x + 8 + 3 = 2x + 11$. 5. **Evaluate $(f \circ g)(-2)$:** - Use the expression from step 3: $2x + 7$. - Substitute $x = -2$: $2(-2) + 7 = -4 + 7 = 3$. 6. **Evaluate $(g \circ f)(-2)$:** - Use the expression from step 4: $2x + 11$. - Substitute $x = -2$: $2(-2) + 11 = -4 + 11 = 7$. **Final answers:** - $(f \circ g)(x) = 2x + 7$ - $(g \circ f)(x) = 2x + 11$ - $(f \circ g)(-2) = 3$ - $(g \circ f)(-2) = 7$