It seems like you're trying to define a function $G(x) = 2x + 6$ and possibly asking to substitute $x = x + 3$ into it.

Let me walk you through this:

Given:

$G(x) = 2x + 6$

Now, if you want to substitute $x = x + 3$ into the function, let's do that step by step.

Substitute $x = x + 3$ into $G(x)$:

$G(x + 3) = 2(x + 3) + 6$

Expand the terms: $G(x + 3) = 2x + 6 + 6$

Simplify: $G(x + 3) = 2x + 12$

So, after the substitution, the new expression for $G(x + 3)$ is: $G(x + 3) = 2x + 12$

Would you like to dive deeper into this concept or have any questions?

Related questions:

1. How do you find the domain and range of the function $G(x)$?
2. What is the graphical interpretation of shifting a function by $x + 3$?
3. How does the slope of the function $G(x) = 2x + 6$ affect its behavior?
4. Can we solve for $x$ if $G(x) = 0$? How?
5. How would $G(x)$ change if we had a different coefficient of $x$?

Tip:

Substituting values or expressions into a function helps you see how the function behaves with different inputs.