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The image shows two functions \( f(x) = x + 2 \) and \( g(x) = 2x + 4 \) under the heading "DIVIDE."

To divide these two functions, we perform the following operation:

\[
\frac{f(x)}{g(x)} = \frac{x + 2}{2x + 4}
\]

Now, simplify the expression:

\[
\frac{x + 2}{2x + 4} = \frac{x + 2}{2(x + 2)}
\]

Since \(x + 2\) appears in both the numerator and the denominator, you can cancel it out, giving:

\[
\frac{f(x)}{g(x)} = \frac{1}{2} \quad \text{for} \quad x \neq -2
\]

The restriction \(x \neq -2\) comes from the fact that \(g(x) = 0\) when \(x = -2\), making the expression undefined at that point.

Would you like any further clarification or details on this process?

Here are 5 related questions to expand your understanding:

1. How do you find the quotient of two more complex functions?
2. What happens when a function is divided by another with no common factors?
3. What is the domain of the function resulting from division?
4. How would you handle the division of polynomial functions?
5. Can the result of a division ever have a removable discontinuity?

**Tip:** Always check for values that would make the denominator zero when simplifying functions!

Divide the functions f(x) = x + 2 and g(x) = 2x + 4.

Learn how to divide the functions f(x) = x + 2 and g(x) = 2x + 4. This involves simplifying the rational expression by canceling common factors, resulting in f(x) / g(x) = 1 / 2 for x ≠ -2. Suitable for students in Grades 9-10.

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