Evaluate the​ expression, ​(gcircle​f)(3​), given the following functions.
​f(x)equalsxplus3 and ​g(x)equalsxsquared
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Part 1
​(gcircle​f)(3​)equals
  
enter your response here. ​(Simplify your​ answer.)

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.

Evaluate the expression, (g∘f)(3), given the following functions: f(x) = x + 3 and g(x) = x^2.

Learn how to evaluate the function composition (g∘f)(3) with functions f(x) = x + 3 and g(x) = x^2. This example explains the steps to compute function compositions, making it a valuable resource for students in Grades 9-10 studying Algebra.

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