1. The problem asks to find the limit $$\lim_{x \to a} [f(x)]^2$$ given that $$\lim_{x \to a} f(x) = -3$$. 2. The formula for the limit of a function raised to a power is: $$\lim_{x \to a} [f(x)]^n = \left(\lim_{x \to a} f(x)\right)^n$$ provided the limit on the right side exists. 3. Since $$\lim_{x \to a} f(x) = -3$$, we can substitute this into the formula: $$\lim_{x \to a} [f(x)]^2 = (-3)^2$$ 4. Calculate the square: $$(-3)^2 = 9$$ 5. Therefore, the limit is: $$\lim_{x \to a} [f(x)]^2 = 9$$ This means as $$x$$ approaches $$a$$, the value of $$[f(x)]^2$$ approaches 9.