1. The problem asks to find the composition of functions $(h \circ g)(x)$, which means $h(g(x))$. 2. Given functions are: $$h(x) = x^2 + 3x$$ $$g(x) = x + 2$$ 3. To find $(h \circ g)(x)$, substitute $g(x)$ into $h(x)$: $$h(g(x)) = h(x + 2)$$ 4. Replace every $x$ in $h(x)$ with $x + 2$: $$h(x + 2) = (x + 2)^2 + 3(x + 2)$$ 5. Expand the square and distribute: $$(x + 2)^2 = x^2 + 4x + 4$$ $$3(x + 2) = 3x + 6$$ 6. Combine the terms: $$h(g(x)) = x^2 + 4x + 4 + 3x + 6 = x^2 + 7x + 10$$ 7. There are no restrictions on $x$ because both $h$ and $g$ are polynomials defined for all real numbers. Final answer: $$(h \circ g)(x) = x^2 + 7x + 10$$