Math Problem Statement
inverse of the function f(x) = 14 - x?
Solution
To find the inverse of the function , follow these steps:
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Replace with :
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Swap and to begin solving for the inverse:
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Solve for :
Thus, the inverse function is:
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:
- How do you find the inverse of a more complex function?
- What are the conditions for a function to have an inverse?
- Can a quadratic function have an inverse? How do you find it?
- What is the geometric interpretation of an inverse function on a graph?
- 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