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

1. **Replace** \( f(x) \) with \( y \):
   \[
   y = 14 - x
   \]
   
2. **Swap** \( x \) and \( y \) to begin solving for the inverse:
   \[
   x = 14 - y
   \]

3. **Solve for** \( y \):
   \[
   y = 14 - x
   \]

Thus, the inverse function is:
\[
f^{-1}(x) = 14 - x
\]

Interestingly, the inverse of this function is the same as the original function itself!

Would you like more details on how inverses of functions work or why this particular function behaves this way?

### Related questions:
1. How do you find the inverse of a more complex function?
2. What are the conditions for a function to have an inverse?
3. Can a quadratic function have an inverse? How do you find it?
4. What is the geometric interpretation of an inverse function on a graph?
5. How does the domain and range of a function relate to its inverse?

**Tip:** When solving for inverses, always check that the original function is one-to-one to ensure the inverse exists!

Learn how to find the inverse of the function f(x) = 14 - x with a simple step-by-step explanation. This solution covers core algebraic concepts like inverse functions, showing that f(x) = 14 - x is its own inverse. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation