To find the composition of the functions \( f \) and \( g \), denoted as \( (f \circ g)(x) \), you need to substitute \( g(x) \) into \( f(x) \). 

Given:
- \( f(x) = 2x - 9 \)
- \( g(x) = -x + 4 \)

Now, calculate \( (f \circ g)(x) \):
\[
(f \circ g)(x) = f(g(x))
\]
Substitute \( g(x) = -x + 4 \) into \( f(x) \):
\[
f(g(x)) = f(-x + 4)
\]
Now, replace \( x \) in \( f(x) = 2x - 9 \) with \( -x + 4 \):
\[
f(-x + 4) = 2(-x + 4) - 9
\]
Distribute and simplify:
\[
f(-x + 4) = -2x + 8 - 9
\]
\[
f(-x + 4) = -2x - 1
\]

So, the composition \( (f \circ g)(x) = -2x - 1 \).

Would you like more details or have any questions?

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

**Tip:** When composing functions, always replace the entire variable in the outer function with the expression from the inner function.

Explore how to find the composition of functions f and g, denoted as (f o g)(x). Learn step-by-step how to substitute g(x) into f(x) to calculate (f o g)(x), with detailed examples and explanations. Suitable for high school students studying functions and algebra.

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