Find the inverse function in slope-intercept form (mx+b):
f, of, x, equals, minus, 2, x, plus, 12
f(x)=
−2x+12

To find the inverse of the function \( f(x) = -2x + 12 \), follow these steps:

### Step 1: Replace \( f(x) \) with \( y \).
\[
y = -2x + 12
\]

### Step 2: Swap \( x \) and \( y \) to find the inverse.
\[
x = -2y + 12
\]

### Step 3: Solve for \( y \).
\[
x - 12 = -2y
\]
\[
y = \frac{x - 12}{-2}
\]
\[
y = -\frac{1}{2}x + 6
\]

### Step 4: Replace \( y \) with \( f^{-1}(x) \) to express the inverse function.
\[
f^{-1}(x) = -\frac{1}{2}x + 6
\]

So, the inverse function in slope-intercept form is:
\[
f^{-1}(x) = -\frac{1}{2}x + 6
\]

Would you like any further details or have any questions about the steps? 

Here are 5 related questions to explore further:

1. How do you verify that two functions are inverses of each other?
2. What are the implications of a function being its own inverse?
3. How do you find the inverse of a quadratic function?
4. What does the slope of the inverse function tell you about the original function?
5. How do you determine if a function is invertible?

**Tip:** The graph of a function and its inverse are symmetric with respect to the line \( y = x \).

Find the inverse function in slope-intercept form (mx+b): f(x) = -2x + 12

Discover how to find the inverse function of f(x) = -2x + 12 in slope-intercept form. This algebra problem involves key concepts such as inverse functions and the slope-intercept form, and is suitable for students in Grades 10-12.

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