Given the definitions of f(x) and g(x) below, find the value of f (g(2)).
f(x) = x2+6x + 11
9x) = -5x + 1

To find the value of \( f(g(2)) \), we'll first compute \( g(2) \) and then substitute that value into the function \( f(x) \).

1. **Step 1: Compute \( g(2) \)**
   \[
   g(x) = -5x + 1
   \]
   Substituting \( x = 2 \):
   \[
   g(2) = -5(2) + 1 = -10 + 1 = -9
   \]

2. **Step 2: Compute \( f(g(2)) = f(-9) \)**
   The function \( f(x) \) is given by:
   \[
   f(x) = x^2 + 6x + 11
   \]
   Now, substitute \( x = -9 \) into \( f(x) \):
   \[
   f(-9) = (-9)^2 + 6(-9) + 11
   \]
   Simplifying:
   \[
   f(-9) = 81 - 54 + 11 = 38
   \]

Therefore, the value of \( f(g(2)) \) is \( \boxed{38} \).

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

Here are 5 related questions to expand your understanding:

1. What would \( f(g(3)) \) be for the same functions?
2. How does changing the function \( g(x) \) affect the overall result of \( f(g(x)) \)?
3. Can you calculate \( f(f(2)) \) for the given \( f(x) \)?
4. What is the graphical interpretation of nested functions like \( f(g(x)) \)?
5. How would the result change if \( f(x) \) were a linear function instead of quadratic?

**Tip:** When working with nested functions, always evaluate the inner function first before substituting into the outer function.

Given the definitions of f(x) and g(x) below, find the value of f(g(2)). f(x) = x^2 + 6x + 11, g(x) = -5x + 1.

Learn how to find the value of f(g(2)) for the functions f(x) = x^2 + 6x + 11 and g(x) = -5x + 1. This step-by-step guide explains function composition and provides a detailed solution, suitable for students in Grades 9-11.

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