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The problem asks to find the formula for the composition of functions \( (g \circ f)(x) \), given:

- \( f(x) = x^2 + 13x + 40 \)
- \( g(x) = x - 5 \)

To find \( (g \circ f)(x) \), we need to substitute \( f(x) \) into \( g(x) \). That is, we replace the \( x \) in \( g(x) \) with the expression for \( f(x) \).

### Step-by-step solution:

1. **Start with the formula for composition:**
   \[
   (g \circ f)(x) = g(f(x))
   \]

2. **Substitute \( f(x) \) into \( g(x) \):**
   \[
   g(f(x)) = g(x^2 + 13x + 40)
   \]

   Since \( g(x) = x - 5 \), we replace the argument \( x \) in \( g(x) \) with \( x^2 + 13x + 40 \):
   \[
   g(f(x)) = (x^2 + 13x + 40) - 5
   \]

3. **Simplify the expression:**
   \[
   g(f(x)) = x^2 + 13x + 40 - 5
   \]
   \[
   g(f(x)) = x^2 + 13x + 35
   \]

So, the formula for \( (g \circ f)(x) \) is:
\[
(g \circ f)(x) = x^2 + 13x + 35
\]

Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:

1. What is the general formula for the composition of two functions?
2. How does composition of functions differ from multiplication of functions?
3. What is the domain of the function \( (g \circ f)(x) \) in this case?
4. Can \( f(x) \) or \( g(x) \) be a more complex function, such as a trigonometric or logarithmic function?
5. How would you compute \( (f \circ g)(x) \), i.e., the composition in reverse order?

**Tip:** Always pay attention to the domain restrictions when composing functions, as certain inputs might not be valid for the composition depending on the individual functions.

Jika f(x) = x^2 + 13x + 40 dan g(x) = x - 5, maka rumus (gof)(x) adalah ...

Learn how to solve the composition of two functions f(x) = x^2 + 13x + 40 and g(x) = x - 5, to find the formula (gof)(x). This solution covers function composition and quadratic equations, suitable for students in Grades 10-12.

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