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.