To find the value of $f(g(2))$, we'll first compute $g(2)$ and then substitute that value into the function $f(x)$.

1. Step 1: Compute $g(2)$ $g(x) = -5x + 1$ Substituting $x = 2$: $g(2) = -5(2) + 1 = -10 + 1 = -9$

2. Step 2: Compute $f(g(2)) = f(-9)$ The function $f(x)$ is given by: $f(x) = x^2 + 6x + 11$ Now, substitute $x = -9$ into $f(x)$: $f(-9) = (-9)^2 + 6(-9) + 11$ Simplifying: $f(-9) = 81 - 54 + 11 = 38$

Therefore, the value of $f(g(2))$ is $\boxed{38}$.

Would you like further details on any step or more explanation?

Here are 5 related questions to expand your understanding:

1. What would $f(g(3))$ be for the same functions?
2. How does changing the function $g(x)$ affect the overall result of $f(g(x))$?
3. Can you calculate $f(f(2))$ for the given $f(x)$?
4. What is the graphical interpretation of nested functions like $f(g(x))$?
5. How would the result change if $f(x)$ were a linear function instead of quadratic?

Tip: When working with nested functions, always evaluate the inner function first before substituting into the outer function.