9. Given g(x) = 6x + 4 and f(x) = 2x - 7 what is g(x) - f(x)?

A. 4x - 3
B. 8x - 3
C. 4x - 11
D. 4x + 11


To solve \( g(x) - f(x) \) given \( g(x) = 6x + 4 \) and \( f(x) = 2x - 7 \), follow these steps:

1. Subtract \( f(x) \) from \( g(x) \):
\[
g(x) - f(x) = (6x + 4) - (2x - 7)
\]

2. Distribute the negative sign to the terms in \( f(x) \):
\[
g(x) - f(x) = 6x + 4 - 2x + 7
\]

3. Combine like terms:
\[
g(x) - f(x) = (6x - 2x) + (4 + 7)
\]
\[
g(x) - f(x) = 4x + 11
\]

So, the correct answer is **D. 4x + 11**.

Would you like more details or have any questions? Here are some related questions you might consider:

1. What is the value of \( g(x) \) at \( x = 2 \)?
2. What is the value of \( f(x) \) at \( x = -1 \)?
3. How do you find the intersection point of \( g(x) \) and \( f(x) \)?
4. If \( h(x) = g(x) + f(x) \), what is the expression for \( h(x) \)?
5. How would the expression change if \( f(x) = 3x - 5 \) instead?

**Tip:** When subtracting functions, be careful with distributing negative signs to avoid errors in combining like terms.

Learn how to subtract functions g(x) = 6x + 4 and f(x) = 2x - 7 with a step-by-step solution. Understand the basics of algebraic functions and the process of subtracting them. Suitable for students in Grades 7-9.

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