https://file.aiquickdraw.com/mathbot/file/1728284898975aduc2qt1.jpg

The function given in the image is \( f(x) = 2x - 4 \) for all \( x \in \mathbb{R} \). The problem asks to find the value of \( x \) for which \( f(x) = 6 \).

Let's solve this:

1. We have the equation \( f(x) = 6 \), and we know \( f(x) = 2x - 4 \).
   
   Therefore, set \( 2x - 4 = 6 \).

2. Solve for \( x \):

   \[
   2x - 4 = 6
   \]
   Add 4 to both sides:
   \[
   2x = 10
   \]
   Divide both sides by 2:
   \[
   x = 5
   \]

So, the value of \( x \) for which \( f(x) = 6 \) is \( x = 5 \).

Would you like further details or explanations on any of the steps?

Here are 5 related questions:
1. How would you solve \( f(x) = 0 \) for this function?
2. What is the inverse of the function \( f(x) = 2x - 4 \)?
3. How does the slope of the function \( f(x) = 2x - 4 \) affect its graph?
4. What is the domain and range of this function?
5. How do linear functions like this one behave as \( x \to \infty \)?

**Tip:** Always check your solutions by substituting the value of \( x \) back into the original function to confirm correctness!

Find the value of x for which f(x) = 6, where f(x) = 2x - 4 for all x in R.

Learn how to solve the linear equation f(x) = 2x - 4 for f(x) = 6 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear equations. Suitable for students in Grades 7-9.

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