Math Problem Statement
For the function f(x) = 9x + 4, find f^{-1}(x).
Solution
We are given the function , and the task is to find the inverse of this function, denoted by .
Steps to find the inverse function:
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Start with the original function: where .
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Swap and to prepare for solving for the inverse:
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Solve for (which will be the inverse function):
So, the inverse function is:
Answer:
The correct option is:
Do you have any further questions or would you like a more detailed explanation?
Related Questions:
- How do you determine if a function has an inverse?
- Can a function have more than one inverse?
- What are the steps to verify that two functions are inverses?
- What is the domain and range of the inverse function?
- How would you graph both the function and its inverse?
Tip: Always check that a function is one-to-one (passes the horizontal line test) before finding its inverse!
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Math Problem Analysis
Mathematical Concepts
Algebra
Inverse Functions
Formulas
f(x) = 9x + 4
f^{-1}(x) = (x - 4)/9
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 9-12