1. **State the problem:** Determine if the functions $y=\frac{1}{3}x+3$ and $y=-3x-3$ are inverses of each other. 2. **Recall the rule for inverse functions:** Two functions $f$ and $g$ are inverses if and only if $f(g(x))=x$ and $g(f(x))=x$ for all $x$ in the domains. 3. **Check $f(g(x))$ where $f(x)=\frac{1}{3}x+3$ and $g(x)=-3x-3$: ** $$f(g(x))=f(-3x-3)=\frac{1}{3}(-3x-3)+3=-x-1+3=-x+2$$ 4. Since $f(g(x))=-x+2 \neq x$, the functions are not inverses. 5. **Check $g(f(x))$ for completeness:** $$g(f(x))=g\left(\frac{1}{3}x+3\right)=-3\left(\frac{1}{3}x+3\right)-3=-x-9-3=-x-12$$ 6. Since $g(f(x))=-x-12 \neq x$, this confirms the functions are not inverses. **Final answer:** The functions $y=\frac{1}{3}x+3$ and $y=-3x-3$ are **not** inverses of each other.