https://file.aiquickdraw.com/mathbot/file/17258116120132g1qbb8a.jpg

To solve the problem, we need to find \(\left(\frac{g}{f}\right)(3)\), which means finding the value of \( \frac{g(3)}{f(3)} \).

Given:
- \( g(a) = 3a + 2 \)
- \( f(a) = 2a - 4 \)

### Step 1: Calculate \( g(3) \)
Substitute \( a = 3 \) into the function \( g(a) \):

\[
g(3) = 3(3) + 2 = 9 + 2 = 11
\]

### Step 2: Calculate \( f(3) \)
Substitute \( a = 3 \) into the function \( f(a) \):

\[
f(3) = 2(3) - 4 = 6 - 4 = 2
\]

### Step 3: Calculate \( \frac{g(3)}{f(3)} \)

\[
\frac{g(3)}{f(3)} = \frac{11}{2}
\]

So, the value of \(\left(\frac{g}{f}\right)(3)\) is \( \frac{11}{2} \) or 5.5.

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### Related Questions:
1. What is the domain of the function \(\frac{g(a)}{f(a)}\)?
2. How would the answer change if \( g(a) \) and \( f(a) \) were different?
3. Can you find the value of \(\left(\frac{f}{g}\right)(3)\)?
4. What are the intercepts of the function \( g(a) = 3a + 2 \)?
5. How do you find the inverse of \( f(a) = 2a - 4 \)?

### Tip:
When working with functions, always substitute carefully to avoid simple calculation errors, especially when dealing with fractions.

Find (g/f)(3) given g(a) = 3a + 2 and f(a) = 2a - 4

Learn how to evaluate (g/f)(3) where g(a) = 3a + 2 and f(a) = 2a - 4. Follow the step-by-step process to find g(3) and f(3), and understand how to divide two functions. Suitable for Grades 9-10.

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