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To solve \( (f \circ g)(x) \), which is the composition of the functions \( f(x) = 3x - 5 \) and \( g(x) = x - 9 \), follow these steps:

### Step 1: Understand function composition.
The composition \( (f \circ g)(x) \) means that we apply \( g(x) \) first, and then use the result as the input to \( f(x) \). In other words:
\[
(f \circ g)(x) = f(g(x))
\]

### Step 2: Substitute \( g(x) \) into \( f(x) \).
Since \( g(x) = x - 9 \), substitute this expression into \( f(x) \):
\[
f(g(x)) = f(x - 9)
\]

Now, recall that \( f(x) = 3x - 5 \). Replace \( x \) in \( f(x) \) with \( x - 9 \):
\[
f(x - 9) = 3(x - 9) - 5
\]

### Step 3: Simplify the expression.
Simplify the expression:
\[
3(x - 9) - 5 = 3x - 27 - 5 = 3x - 32
\]

Thus, the expression equivalent to \( (f \circ g)(x) \) is:
\[
(f \circ g)(x) = 3x - 32
\]

Would you like more details or have any questions?

### Related Questions:
1. What would \( (g \circ f)(x) \) look like with the same functions?
2. How do you evaluate \( (f \circ g)(2) \)?
3. What happens if you change the functions to non-linear forms, like \( f(x) = x^2 \)?
4. Can you find the domain of the composed function \( (f \circ g)(x) \)?
5. How would this composition work if \( g(x) \) was a trigonometric function?

### Tip:
When performing function composition, always start by substituting the inner function's output as the input to the outer function, and carefully simplify the result.

If f(x) = 3x - 5 and g(x) = x - 9, which expression is equivalent to (f o g)(x)?

Learn how to solve the function composition (f o g)(x) where f(x) = 3x - 5 and g(x) = x - 9. This step-by-step guide covers key algebraic concepts, ideal for students in Grades 9-11.

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