https://file.aiquickdraw.com/mathbot/file/17254396391936tom88ry.jpg

Let's analyze the problem from the image:

You're given the functions \( g(a) = -2a + 5 \) and \( f(a) = 3a + 5 \). You are asked to find \( \left(\frac{g}{f}\right)(a) \).

This expression means you need to divide the function \( g(a) \) by the function \( f(a) \).

### Step 1: Write down the functions
- \( g(a) = -2a + 5 \)
- \( f(a) = 3a + 5 \)

### Step 2: Set up the division
\[
\left(\frac{g}{f}\right)(a) = \frac{g(a)}{f(a)} = \frac{-2a + 5}{3a + 5}
\]

### Final Answer:
The result is:
\[
\left(\frac{g}{f}\right)(a) = \frac{-2a + 5}{3a + 5}
\]

Would you like further details on this problem or have any questions? Here are some related questions you might find helpful:

1. How would you simplify \( \left(\frac{g}{f}\right)(a) \) further if possible?
2. What is the domain of \( \left(\frac{g}{f}\right)(a) \)?
3. How do you determine when \( \left(\frac{g}{f}\right)(a) = 0 \)?
4. Can the expression \( \left(\frac{g}{f}\right)(a) \) be rewritten in a different form?
5. How do you interpret \( \left(\frac{g}{f}\right)(a) \) graphically?

**Tip:** When dividing functions, always consider the domain of the resulting function to ensure it is defined for all possible values.

Given g(a) = -2a + 5 and f(a) = 3a + 5, find (g/f)(a).

Learn how to find the quotient of two functions using the example g(a) = -2a + 5 and f(a) = 3a + 5. This problem involves key algebraic concepts such as function operations and rational functions. Suitable for students in Grades 9-12.

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