1. **State the problem:** We are given two functions: $$f(x) = -4x^2 - 3$$ $$g(x) = 3x - 3$$ We need to find the values of $f(5)$ and $g(-3)$. 2. **Recall the evaluation rule:** To find $f(a)$, substitute $x = a$ into the function $f(x)$ and simplify. 3. **Evaluate $f(5)$:** $$f(5) = -4(5)^2 - 3$$ Calculate the square: $$5^2 = 25$$ Substitute: $$f(5) = -4 \times 25 - 3 = -100 - 3 = -103$$ 4. **Evaluate $g(-3)$:** $$g(-3) = 3(-3) - 3$$ Multiply: $$3 \times (-3) = -9$$ Substitute: $$g(-3) = -9 - 3 = -12$$ **Final answers:** $$f(5) = -103$$ $$g(-3) = -12$$