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Part 1
Suppose that ​f(x)equals=77xplus+11 and ​g(x)equals=minus−77xplus+33. Complete parts ​(a) through ​(d).
Question content area bottom
Part 1
​(a) Determine an algebraic expression for ​f(x)minus−​g(x) by subtracting​ g(x) from​ f(x) and combining like terms.
​f(x)minus−​g(x)equals=enter your response here ​(Simplify your answer. Do not​ factor.)

To determine \( f(x) - g(x) \), we need to subtract the expression for \( g(x) \) from \( f(x) \) and combine like terms.

Given:
- \( f(x) = 77x + 11 \)
- \( g(x) = -77x + 33 \)

Now, subtract \( g(x) \) from \( f(x) \):

\[
f(x) - g(x) = (77x + 11) - (-77x + 33)
\]

Distribute the negative sign:

\[
f(x) - g(x) = 77x + 11 + 77x - 33
\]

Combine the like terms:

\[
f(x) - g(x) = (77x + 77x) + (11 - 33)
\]

\[
f(x) - g(x) = 154x - 22
\]

So, the simplified expression for \( f(x) - g(x) \) is:

\[
f(x) - g(x) = 154x - 22
\]

Would you like more details or have any questions? 

Here are five related questions to expand on this topic:
1. What is \( f(x) + g(x) \) if \( f(x) = 77x + 11 \) and \( g(x) = -77x + 33 \)?
2. How do you determine \( f(x) \times g(x) \) for the given functions?
3. What happens when \( f(x) = g(x) \)? What value of \( x \) makes this true?
4. How does the behavior of \( f(x) \) and \( g(x) \) change as \( x \) approaches infinity?
5. Can you find the inverse of \( f(x) = 77x + 11 \)?

**Tip:** When subtracting polynomials, always distribute negative signs carefully to avoid errors.

Suppose that f(x) = 77x + 11 and g(x) = -77x + 33. Complete parts (a) through (d). (a) Determine an algebraic expression for f(x) - g(x) by subtracting g(x) from f(x) and combining like terms.

Explore the process of subtracting two polynomial functions, f(x) = 77x + 11 and g(x) = -77x + 33. Learn how to apply the distributive property and combine like terms to find the expression f(x) - g(x). This problem covers core algebraic techniques suitable for students in Grades 9-11.

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