We are given the functions $f(x)$ and $g(x)$:

• $f(x) = 2x^2 - x - 9$
• $g(x) = 4x + 1$

To find $g(f(2))$, we will follow these steps:

Step 1: Find $f(2)$

Substitute $x = 2$ into the function $f(x)$: $f(2) = 2(2)^2 - (2) - 9$ $f(2) = 2(4) - 2 - 9 = 8 - 2 - 9 = -3$

Step 2: Find $g(f(2))$ or $g(-3)$

Now substitute $f(2) = -3$ into $g(x)$: $g(-3) = 4(-3) + 1 = -12 + 1 = -11$

Final Answer:

The value of $g(f(2))$ is $\boxed{-11}$.

Would you like more details on any of these steps, or do you have any other questions?

Here are 5 related questions for practice:

1. Find $g(f(3))$ using the same functions.
2. If $f(x) = 2x^2 - x - 9$, what is $f(-1)$?
3. If $g(x) = 4x + 1$, what is $g(5)$?
4. Solve for $x$ if $f(x) = 0$.
5. What is the composition $f(g(x))$?

Tip: When evaluating compositions like $g(f(x))$, always start by finding the inner function first and then apply the outer function.