Math Problem Statement

inverse of the function f(x) = 14 - x?

Solution

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

  1. Replace f(x)f(x) with yy: y=14xy = 14 - x

  2. Swap xx and yy to begin solving for the inverse: x=14yx = 14 - y

  3. Solve for yy: y=14xy = 14 - x

Thus, the inverse function is: f1(x)=14xf^{-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!

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Inverse Functions

Formulas

f(x) = 14 - x
f^{-1}(x) = 14 - x

Theorems

The Inverse Function Theorem

Suitable Grade Level

Grades 8-10