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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