Math Problem Statement
f^(-1)(x)=(1)/(\sqrt(3-2x))
Solution
You have given the function , which represents the inverse of some original function . Now, if we want to find the original function , we need to follow these steps to reverse the inverse process.
Steps to find :
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Start with the inverse function: where .
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Swap and to reverse the function:
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Solve for (which will now represent ):
Multiply both sides by to eliminate the denominator:
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Divide both sides by :
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Square both sides to remove the square root:
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Isolate by subtracting 3 from both sides:
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Finally, divide by to solve for :
Thus, the original function is:
Would you like further details on any part of this process, or do you have any questions?
Here are some related questions for practice:
- What is the domain of the function ?
- How would you verify that ?
- What are the restrictions on for the original function ?
- How does the graph of compare to the graph of ?
- Can or have any horizontal asymptotes?
Tip: When dealing with inverse functions, always check the domain and range carefully since they are swapped between the function and its inverse.
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Algebra
Radical Equations
Formulas
y = 1/√(3 - 2x)
f(f^{-1}(x)) = x
Theorems
Properties of Inverse Functions
Square Root Properties
Suitable Grade Level
Grades 10-12