Given the functions:
- \( f(x) = x \)
- \( g(x) = 12f(x) \)

To express \( g(x) \) more clearly, you can substitute the expression for \( f(x) \) into \( g(x) \):

\[
g(x) = 12f(x) = 12 \times x = 12x
\]

So, \( g(x) = 12x \).

Would you like more details or have any questions?

Here are five questions that extend this topic:
1. What happens if you combine \( f(x) \) and \( g(x) \) through addition or multiplication?
2. How would you find the derivative of \( f(x) \) and \( g(x) \)?
3. Can you express the composition of the two functions, i.e., \( g(f(x)) \)?
4. How would these functions behave if they were shifted vertically or horizontally?
5. What is the inverse of \( g(x) \)?

**Tip:** For linear functions like \( f(x) = x \) and \( g(x) = 12x \), their graphs are straight lines. The slope of the line represents the rate of change, which for \( f(x) \) is 1, and for \( g(x) \) is 12.

Understand how to solve the linear functions f(x)=x and g(x)=12f(x), where g(x) is expressed in terms of f(x). This example demonstrates key concepts in algebra, including linear function manipulation and function composition. Perfect for students in Grades 6-8.

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