**If  f(x) = x+4  and  g(x) = 2x2-x-1, evaluate the composition (g o f)(2).**


To evaluate the composition \((g \circ f)(2)\), we need to follow these steps:

1. **First, calculate \( f(2) \):**
   \[
   f(x) = x + 4
   \]
   Substituting \( x = 2 \):
   \[
   f(2) = 2 + 4 = 6
   \]

2. **Now, calculate \( g(f(2)) \), which is \( g(6) \):**
   \[
   g(x) = 2x^2 - x - 1
   \]
   Substituting \( x = 6 \):
   \[
   g(6) = 2(6)^2 - 6 - 1
   \]
   Simplifying:
   \[
   g(6) = 2(36) - 6 - 1 = 72 - 6 - 1 = 65
   \]

Therefore, \((g \circ f)(2) = 65\).

Would you like any further details on this process or any other questions?

### Related Questions:
1. How do you evaluate compositions of functions in general?
2. What happens if you reverse the composition, i.e., evaluate \( (f \circ g)(2) \)?
3. Can you explain how to find the domain of a composite function?
4. How would the result change if \( f(x) = x^2 + 4 \) instead of \( f(x) = x + 4 \)?
5. What are some applications of function compositions in real-world problems?

### Tip:
When composing functions, always evaluate the inner function first, and use its result as the input for the outer function.

If f(x) = x + 4 and g(x) = 2x^2 - x - 1, evaluate the composition (g o f)(2).

Learn how to evaluate the composition of two functions, f(x) = x + 4 and g(x) = 2x^2 - x - 1, at x = 2. This step-by-step guide covers function composition and quadratic functions. Suitable for students in Grades 9-11.

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