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


To solve the composition \((g \circ f)(2)\), we first need to find the value of \(f(2)\) and then use this result to evaluate \(g(f(2))\).

### Step 1: Find \(f(2)\)

The function \(f(x) = x + 4\).

\[
f(2) = 2 + 4 = 6
\]

### Step 2: Evaluate \(g(f(2)) = g(6)\)

Now we need to find \(g(6)\) using the function \(g(x) = 2x^2 - x - 1\).

\[
g(6) = 2(6)^2 - 6 - 1
\]

Calculate \(6^2\):

\[
6^2 = 36
\]

Substitute back into the equation:

\[
g(6) = 2(36) - 6 - 1 = 72 - 6 - 1 = 65
\]

### Final Answer

\[
(g \circ f)(2) = g(f(2)) = g(6) = 65
\]

So, the value of the composition \((g \circ f)(2)\) is **65**.

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1. What is the definition of a function composition?
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If f(x) = x+4 and g(x) = 2x^2 - x - 1, evaluate the composition (g o f)(2).

Learn how to evaluate the function composition (g o f)(2) where f(x) = x + 4 and g(x) = 2x^2 - x - 1. This step-by-step guide covers function composition, algebra, and quadratic functions. Suitable for students in Grades 9-10.

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