Given the function f, of, x, equals, minus, x, minus, 2f(x)=−x−2, then what is f, of, x, minus, 3f(x)−3 as a simplified polynomial?

We are given the function:

\[
f(x) = -x - 2
\]

The task is to find the simplified expression for:

\[
f(x) - 3f(x) - 3
\]

### Step 1: Substitute \( f(x) \) in the expression.

We know that \( f(x) = -x - 2 \). So, substitute this into the expression:

\[
f(x) - 3f(x) - 3 = (-x - 2) - 3(-x - 2) - 3
\]

### Step 2: Simplify the expression.

Distribute the \( -3 \) to the terms inside the parentheses:

\[
= (-x - 2) - 3(-x) - 3(-2) - 3
\]
\[
= (-x - 2) + 3x + 6 - 3
\]

### Step 3: Combine like terms.

\[
= -x + 3x - 2 + 6 - 3
\]

Simplify:

\[
= 2x + 1
\]

### Final Answer:
The simplified polynomial is:

\[
2x + 1
\]

Would you like more details, or do you have any questions?

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Here are 5 related questions to explore:
1. How do you find the value of \( f(x) \) at a specific point?
2. What happens if you modify \( f(x) \) by multiplying it by a constant?
3. How do you simplify a polynomial involving multiple terms?
4. What is the effect of distributing negative signs in expressions?
5. How do you solve equations involving functions and constants?

**Tip:** Always distribute carefully when working with negative coefficients to avoid sign errors.

Given the function f(x) = -x - 2, then what is f(x) - 3f(x) - 3 as a simplified polynomial?

Learn how to simplify the polynomial expression f(x) - 3f(x) - 3, given the function f(x) = -x - 2. This detailed step-by-step solution covers key algebraic concepts like function substitution and polynomial simplification. Suitable for students in Grades 9-10.

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