For the given functions f and​ g, find the following and state the domain of each result.
f left parenthesis x right parenthesis equals 5 x plus 7​; g left parenthesis x right parenthesis equals 3 x minus 5
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Part 1
​(a)  left parenthesis f minus g right parenthesis left parenthesis x right parenthesis equals
  
enter your response here


Given the functions:

- \( f(x) = 5x + 7 \)
- \( g(x) = 3x - 5 \)

We need to find \( (f - g)(x) \).

### Step 1: Subtract \( g(x) \) from \( f(x) \)
\[
(f - g)(x) = f(x) - g(x)
\]

Substituting the given functions:

\[
(f - g)(x) = (5x + 7) - (3x - 5)
\]

### Step 2: Simplify the expression
\[
(f - g)(x) = 5x + 7 - 3x + 5
\]
\[
(f - g)(x) = (5x - 3x) + (7 + 5)
\]
\[
(f - g)(x) = 2x + 12
\]

### Final answer:
\[
(f - g)(x) = 2x + 12
\]

### Domain:
Both \( f(x) \) and \( g(x) \) are linear functions, and the subtraction of two linear functions is also linear. Therefore, the domain is all real numbers:
\[
\text{Domain of } (f - g)(x): \ (-\infty, \infty)
\]

Would you like details on any step, or have any questions?

Here are 5 related questions:
1. What is \( (f + g)(x) \) for the same functions?
2. How do you find the domain of a function with a square root?
3. What is the product of \( f(x) \) and \( g(x) \)?
4. What is the composition \( f(g(x)) \)?
5. How do you find the inverse of a function?

**Tip**: Always simplify step-by-step, especially when dealing with multiple terms!

For the given functions f and g, find the following and state the domain of each result.

f(x) = 5x + 7; g(x) = 3x - 5

(a) (f - g)(x) = ?

Learn how to subtract the functions f(x) = 5x + 7 and g(x) = 3x - 5 to find (f - g)(x). This problem demonstrates how to simplify linear equations step-by-step and determine the domain. Suitable for students in Grades 9-10.

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