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