The given function is $f(x) = \cos(x^2 + x)$.

We are asked to find $f(2)$, which means substituting $x = 2$ into the function.

Steps:

1. Substitute $x = 2$ into the expression for $f(x)$: $f(2) = \cos(2^2 + 2) = \cos(4 + 2) = \cos(6)$

Thus, the value of $f(2)$ is $\cos(6)$, which corresponds to option (d).

Answer:

(d) $\cos(6)$

Would you like a further breakdown of this calculation or have any related questions?

Here are 5 related questions for deeper understanding:

1. What is the general formula for differentiating trigonometric functions like cosine?
2. How does the chain rule apply to functions like $f(x) = \cos(g(x))$?
3. What is the periodicity of the cosine function, and how does it affect values like $\cos(6)$?
4. Can you evaluate $\cos(6)$ using a calculator or approximate the value manually?
5. What happens if you change the function to $f(x) = \sin(x^2 + x)$? How would the answer change?

Tip: For functions involving trigonometric terms, always double-check your substitution steps carefully to avoid small mistakes.