The function \( (f \circ g)(x) \) represents the composition of \( f(x) \) and \( g(x) \), which means you plug \( g(x) \) into \( f(x) \). Here's the process:

1. You are given:
   - \( f(x) = 2x \)
   - \( g(x) = x + 5 \)

2. To find \( (f \circ g)(x) \), substitute \( g(x) \) into \( f(x) \):
   \[
   (f \circ g)(x) = f(g(x)) = f(x + 5)
   \]

3. Now, use the definition of \( f(x) = 2x \), but instead of \( x \), replace it with \( x + 5 \):
   \[
   f(x + 5) = 2(x + 5)
   \]

4. Simplify:
   \[
   2(x + 5) = 2x + 10
   \]

Thus, \( (f \circ g)(x) = 2x + 10 \).

Would you like more details or further explanation?

Here are 5 related questions:
1. What is \( (g \circ f)(x) \)?
2. Can you graph \( f(x) = 2x \) and \( g(x) = x + 5 \) to see how they interact?
3. How do compositions of functions change if you reverse the order?
4. What happens when you compose functions with inverse functions?
5. How does function composition relate to real-world applications?

**Tip:** When composing functions, always substitute the inner function into the outer one carefully to avoid mistakes!

f(x) = 2x and g(x) = x + 5, find (f ° g)(x)

Learn how to find the composition of two linear functions, f(x) = 2x and g(x) = x + 5, and calculate (f ° g)(x) with a detailed step-by-step solution. This problem covers key algebraic concepts such as function composition, suitable for students in Grades 9-10.

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