To evaluate $(g \circ f)(3)$, we need to understand that this represents the composition of two functions, $g(f(x))$. We’ll first find $f(3)$ and then apply $g$ to the result of $f(3)$.

Given:

• $f(x) = x + 3$
• $g(x) = x^2$

Step 1: Evaluate $f(3)$

$f(3) = 3 + 3 = 6$

Step 2: Substitute $f(3)$ into $g$

Now, we want to find $g(f(3)) = g(6)$. $g(6) = 6^2 = 36$

Final Answer:

$(g \circ f)(3) = 36$

Would you like a detailed explanation of function composition or have any other questions?

Here are some related questions:

1. What is function composition and how does it work?
2. How do we evaluate compositions when given two functions in general?
3. If $h(x) = x - 2$, what would $(f \circ h)(5)$ be?
4. How does the order of functions in composition (like $g \circ f$ vs. $f \circ g$) affect the result?
5. Can we extend this concept to more than two functions?

Tip: When working with function compositions, always evaluate the inner function first before applying the outer function.