Math Problem Statement
How do I find the inverse of this
Solution
To find the inverse of the function in the given image, let’s break down the process step by step. The function provided is:
We will determine the inverse as follows:
Steps to Find the Inverse:
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Replace with :
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Swap and : This step is crucial because the inverse function reflects and in the equation:
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Solve for : Rearrange the equation to isolate :
- Multiply both sides by to remove the denominator:
- Expand:
- Move all terms involving to one side:
- Factor out on the right-hand side:
- Solve for :
Final Answer:
The inverse function is:
Let me know if you'd like me to verify the result or if you have any additional questions! Below are some related problems for practice.
Related Questions:
- How can you confirm that and are truly inverses of each other?
- What is the domain of ?
- What is the domain of ?
- If , what is ?
- How does the graph of relate to the graph of its inverse?
Tip:
When solving for the inverse, always check for restrictions in the domain to avoid division by zero or other undefined operations.
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Rational Equations
Algebra
Formulas
y = (ax + b) / (cx + d)
Inverse formula by swapping x and y: x = (ay + b) / (cy + d)
Theorems
Definition of an Inverse Function
Suitable Grade Level
Grades 10-12