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We are tasked with finding \((f \circ g)(x)\), which represents the composition of the functions \(f(x)\) and \(g(x)\).

Given:
- \(f(x) = 2x + 3\)
- \(g(x) = x^2\)

### Steps to find \((f \circ g)(x)\):

1. By definition, \((f \circ g)(x) = f(g(x))\).
2. Substitute \(g(x)\) into \(f(x)\). That means replacing the \(x\) in \(f(x)\) with \(g(x)\).

So:
\[
(f \circ g)(x) = f(g(x)) = f(x^2)
\]

3. Now, substitute \(x^2\) into \(f(x) = 2x + 3\):

\[
f(x^2) = 2(x^2) + 3
\]

4. Simplify the expression:

\[
f(x^2) = 2x^2 + 3
\]

Thus, \((f \circ g)(x) = 2x^2 + 3\).

Would you like further clarification or more details on function compositions?

### Related questions:
1. How do you find the composition of three functions?
2. What are the domain and range of \(f \circ g\) given the functions \(f(x) = 2x + 3\) and \(g(x) = x^2\)?
3. How does the order of composition affect the result, i.e., \(f(g(x))\) versus \(g(f(x))\)?
4. What is the graphical interpretation of the composition of two functions?
5. Can a composition of functions ever be undefined, and under what conditions?

**Tip:** Always check the domain of each function before composing to ensure the composition is valid for all \(x\).

Find (f ∘ g)(x). f(x) = 2x + 3, g(x) = x^2.

Learn how to find the composition of functions (f ∘ g)(x) where f(x) = 2x + 3 and g(x) = x^2. This step-by-step guide walks through the function composition process, focusing on algebraic operations. Suitable for students in Grades 9-11.

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