We are given the function \( g(x) = 3 - 2x \). To find \( g(g(x)) \), we need to substitute \( g(x) \) into itself. Here's the step-by-step process:

1. Start with the expression for \( g(x) \):
   \[
   g(x) = 3 - 2x
   \]
2. Now, substitute \( g(x) \) into itself:
   \[
   g(g(x)) = g(3 - 2x)
   \]
3. To find \( g(3 - 2x) \), replace \( x \) in the expression \( g(x) = 3 - 2x \) with \( 3 - 2x \):
   \[
   g(g(x)) = 3 - 2(3 - 2x)
   \]
4. Distribute the \( -2 \) on the right-hand side:
   \[
   g(g(x)) = 3 - 6 + 4x
   \]
5. Simplify the result:
   \[
   g(g(x)) = -3 + 4x
   \]

Thus, \( g(g(x)) = 4x - 3 \).

Would you like more details or have any questions?

Here are some related questions:
1. What is \( g(g(g(x))) \)?
2. How do we determine the inverse of \( g(x) \)?
3. If \( g(x) = 3 - 2x \), what is the value of \( g(5) \)?
4. What happens when we compose two different functions, say \( g(x) \) and \( f(x) \)?
5. How do you find the domain of \( g(x) \)?

**Tip:** When composing functions, remember to substitute the entire expression of one function into the other, keeping track of variables carefully!

This page explains how to compute g(g(x)) when g(x) = 3 - 2x through step-by-step instructions. It covers essential algebraic concepts, such as function composition, and is suitable for students in Grades 8-10.

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