Given g, of, x, equals, minus, x, plus, 4g(x)=−x+4, find g, of, minus, 6g(−6).

We are given the function \( g(x) = -x + 4 \) and are asked to find \( g(-6) \).

To do this, we substitute \( x = -6 \) into the function \( g(x) \):

\[
g(-6) = -(-6) + 4
\]

Simplifying:

\[
g(-6) = 6 + 4 = 10
\]

So, \( g(-6) = 10 \).

Let me know if you want further explanation or have questions.

Here are 5 related questions:
1. How would you solve \( g(3) \) for \( g(x) = -x + 4 \)?
2. Can you find the inverse of the function \( g(x) = -x + 4 \)?
3. What is the domain and range of the function \( g(x) = -x + 4 \)?
4. How do you determine whether \( g(x) = -x + 4 \) is a one-to-one function?
5. What does the graph of \( g(x) = -x + 4 \) look like?

**Tip:** When working with linear functions, remember that substituting values into the function will always yield the corresponding y-values on the graph of that function.

Learn how to evaluate the linear function g(x) = -x + 4 by substituting x = -6. This step-by-step solution covers core algebraic concepts like function evaluation and linear functions. Suitable for students in Grades 6-8.

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