To solve $g(a+3)$ for the given function $g(x) = x^2 + 4x - 2$, we substitute $a+3$ into the function $g(x)$ in place of $x$.

$g(a+3) = (a+3)^2 + 4(a+3) - 2$

Step 1: Expand $(a+3)^2$

$(a+3)^2 = a^2 + 6a + 9$

Step 2: Expand $4(a+3)$

$4(a+3) = 4a + 12$

Step 3: Combine everything

$g(a+3) = (a^2 + 6a + 9) + (4a + 12) - 2$

Step 4: Simplify

$g(a+3) = a^2 + 6a + 9 + 4a + 12 - 2$ $g(a+3) = a^2 + 10a + 19$

Thus, $g(a+3) = a^2 + 10a + 19$.

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you find the derivative of $g(x) = x^2 + 4x - 2$?
2. What is the value of $g(2)$ for the given function?
3. How can you find the roots of the quadratic function $g(x) = x^2 + 4x - 2$?
4. What is the vertex of the parabola described by $g(x) = x^2 + 4x - 2$?
5. How does the function $g(x) = x^2 + 4x - 2$ shift when you graph $g(x+3)$?

Tip: When substituting values into functions, always simplify step by step to avoid mistakes in the process.