Find the inverse function in slope-intercept form (mx+b):
f, of, x, equals, 2, x, minus, 14
f(x)=
2x−14

To find the inverse of the function \( f(x) = 2x - 14 \), follow these steps:

### Step 1: Replace \( f(x) \) with \( y \)
We begin by rewriting the function in terms of \( y \).

\[
y = 2x - 14
\]

### Step 2: Swap \( x \) and \( y \)
Now, switch \( x \) and \( y \) to find the inverse function:

\[
x = 2y - 14
\]

### Step 3: Solve for \( y \)
Next, solve for \( y \):

\[
x + 14 = 2y
\]

\[
y = \frac{x + 14}{2}
\]

### Step 4: Replace \( y \) with \( f^{-1}(x) \)
Now, write the inverse function as:

\[
f^{-1}(x) = \frac{x + 14}{2}
\]

### Final Answer in slope-intercept form:
\[
f^{-1}(x) = \frac{1}{2}x + 7
\]

Would you like more details or have any questions about this process?

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Here are 5 related questions to expand your understanding:

1. How do you verify that two functions are inverses of each other?
2. What is the geometric interpretation of a function and its inverse?
3. How would you find the inverse of a quadratic function?
4. Can every function have an inverse? Why or why not?
5. What is the domain and range of \( f^{-1}(x) = \frac{1}{2}x + 7 \)?

**Tip:** When finding an inverse function, always make sure the original function is one-to-one to ensure the inverse exists.

Find the inverse function in slope-intercept form (mx+b): f(x) = 2x - 14

This tutorial explains how to find the inverse of the linear function f(x) = 2x - 14. Follow a step-by-step process to express the inverse function in slope-intercept form. Perfect for high school students in Grades 9-12 who are studying algebra and inverse functions.

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