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To solve the given problem, let's start by defining the functions \( r(x) \) and \( s(x) \) based on the information provided:

\[
r(x) = 4x - 6
\]
\[
s(x) = 6x
\]

### 1. Expression for \((s + r)(x)\):

\[
(s + r)(x) = s(x) + r(x)
\]
\[
(s + r)(x) = 6x + (4x - 6)
\]
\[
(s + r)(x) = 6x + 4x - 6
\]
\[
(s + r)(x) = 10x - 6
\]

### 2. Expression for \((s - r)(x)\):

\[
(s - r)(x) = s(x) - r(x)
\]
\[
(s - r)(x) = 6x - (4x - 6)
\]
\[
(s - r)(x) = 6x - 4x + 6
\]
\[
(s - r)(x) = 2x + 6
\]

### 3. Evaluate \((s \cdot r)(1)\):

First, we need to find \( r(1) \) and \( s(1) \):

\[
r(1) = 4(1) - 6 = 4 - 6 = -2
\]
\[
s(1) = 6(1) = 6
\]

Now, multiply these values:

\[
(s \cdot r)(1) = s(1) \cdot r(1) = 6 \cdot (-2) = -12
\]

### Summary:
- \((s + r)(x) = 10x - 6\)
- \((s - r)(x) = 2x + 6\)
- \((s \cdot r)(1) = -12\)

Would you like any additional details or have any other questions? Here are some related questions you might be interested in:

1. How to find the inverse of a function?
2. What are the properties of polynomial functions?
3. How do you determine the domain and range of a function?
4. What is the composition of functions and how is it performed?
5. How to solve quadratic equations by factoring?

**Tip:** When combining functions,

Explore how to add, subtract, and multiply functions with detailed examples and solutions. Learn about function operations including addition, subtraction, and multiplication, illustrated through practical examples and step-by-step solutions. Suitable for Grades 9-12 students.

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