To find \( f(g(x)) \), also known as the composition \( f \circ g(x) \), you substitute \( g(x) \) into \( f(x) \).

Given:

- \( f(x) = x^2 - 3x \)
- \( g(x) = x - 3 \)

Step-by-step:

1. Start by substituting \( g(x) = x - 3 \) into \( f(x) \).
   
   \[
   f(g(x)) = f(x - 3)
   \]

2. Now, replace every occurrence of \( x \) in \( f(x) = x^2 - 3x \) with \( (x - 3) \).

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

3. Simplify:

   \[
   (x - 3)^2 = x^2 - 6x + 9
   \]
   \[
   -3(x - 3) = -3x + 9
   \]

4. Combine the terms:

   \[
   f(g(x)) = x^2 - 6x + 9 - 3x + 9
   \]
   \[
   f(g(x)) = x^2 - 9x + 18
   \]

Thus, \( f(g(x)) = x^2 - 9x + 18 \).

Would you like further clarification or more details on any step?

Here are 5 related questions:
1. How do you find \( g(f(x)) \)?
2. What is the domain of the function \( f(g(x)) \)?
3. Can you graph \( f

Discover how to find the composition of functions, specifically f(g(x)) for the functions f(x)=x^2-3x and g(x)=x-3. This step-by-step guide covers essential algebraic concepts like function composition and quadratic expansion, suitable for students in Grades 8-10.

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