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Let's solve the given problems step-by-step. The functions provided are:

\[
f(x) = x - 9
\]
\[
g(x) = 6x^2
\]

### (e) Find \((f + g)(3)\):
\[
(f + g)(x) = f(x) + g(x) = (x - 9) + 6x^2
\]

Plugging in \( x = 3 \):
\[
(f + g)(3) = (3 - 9) + 6 \times 3^2
\]
\[
(f + g)(3) = -6 + 6 \times 9
\]
\[
(f + g)(3) = -6 + 54 = 48
\]

**Answer for (e):** \((f + g)(3) = 48\)

### (f) Find \((f - g)(2)\):
\[
(f - g)(x) = f(x) - g(x) = (x - 9) - 6x^2
\]

Plugging in \( x = 2 \):
\[
(f - g)(2) = (2 - 9) - 6 \times 2^2
\]
\[
(f - g)(2) = -7 - 6 \times 4
\]
\[
(f - g)(2) = -7 - 24 = -31
\]

**Answer for (f):** \((f - g)(2) = -31\)

### (g) Find \((f \cdot g)(4)\):
\[
(f \cdot g)(x) = f(x) \cdot g(x) = (x - 9) \cdot 6x^2
\]

Plugging in \( x = 4 \):
\[
(f \cdot g)(4) = (4 - 9) \cdot 6 \times 4^2
\]
\[
(f \cdot g)(4) = -5 \cdot 6 \times 16
\]
\[
(f \cdot g)(4) = -5 \cdot 96 = -480
\]

**Answer for (g):** \((f \cdot g)(4) = -480\)

### (h) Find \(\left(\frac{f}{g}\right)(1)\):
\[
\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} = \frac{x - 9}{6x^2}
\]

Plugging in \( x = 1 \):
\[
\left(\frac{f}{g}\right)(1) = \frac{1 - 9}{6 \times 1^2}
\]
\[
\left(\frac{f}{g}\right)(1) = \frac{-8}{6}
\]
\[
\left(\frac{f}{g}\right)(1) = -\frac{4}{3}
\]

**Answer for (h):** \(\left(\frac{f}{g}\right)(1) = -\frac{4}{3}\)

---

Do you need any more details or have any questions? Here are some related questions:

1. What is the domain of the function \(\left(\frac{f}{g}\right)(x)\)?
2. How would you find \((f + g)(x)\) in its simplified form?
3. What is the value of \((f - g)(x)\) when \( x = 0 \)?
4. Can you find the zeros of the function \(g(x)\)?
5. What would be the derivative of \(f(x)\) and \(g(x)\)?

**Tip:** Always verify the domain of your function, especially when dealing with divisions to avoid undefined values.

For the given functions f(x) = x - 9 and g(x) = 6x^2, complete parts (a) to (h). (e) Find (f + g)(3), (f) Find (f - g)(2), (g) Find (f ⋅ g)(4), (h) Find (f/g)(1).

Learn how to perform function operations such as addition, subtraction, multiplication, and division for the functions f(x) = x - 9 and g(x) = 6x². This problem covers key algebraic concepts and function manipulation suitable for students in Grades 9-11.

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