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.

Would you like more details or have any questions?

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.