Find the domain of the function.
f left parenthesis x right parenthesis equals negative 7 x plus 7

To find the domain of the function \( f(x) = -7x + 7 \), we need to determine the set of all possible values of \( x \) for which the function is defined.

### Function Analysis:
The given function is:
\[
f(x) = -7x + 7
\]

This is a linear function, which means it is defined for all real numbers. Linear functions do not have any restrictions such as division by zero or square roots of negative numbers, which can limit the domain.

### Conclusion:
Since there are no restrictions on the variable \( x \), the domain of the function is:

\[
\text{Domain of } f(x) = (-\infty, \infty)
\]

or simply, all real numbers.

Would you like more details or have any other questions?

### Related Questions:

1. What is the range of the function \( f(x) = -7x + 7 \)?
2. How would you find the domain of a rational function?
3. What are the key characteristics of linear functions?
4. How do you determine the domain of a function involving square roots?
5. Can you find the x-intercept and y-intercept of the function \( f(x) = -7x + 7 \)?

**Tip:** Always check for operations like division by zero or taking the square root of negative numbers to find the domain of a function.

Find the domain of the function f(x) = -7x + 7.

Learn how to find the domain of the linear function f(x) = -7x + 7. This problem explains the concept of domain for linear functions and shows why the domain is all real numbers. Suitable for students in Grades 9-12.

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