Math Problem Statement
State the inverse function g(x) of this equation: g(x)=3x-2
Solution
To find the inverse of the function , we follow these steps:
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Rewrite the function using instead of :
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Swap and to begin the process of finding the inverse:
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Solve for (which will be ):
Thus, the inverse function is:
Would you like any further details or explanations?
Here are five related questions to further explore the concept of inverse functions:
- How can you verify if two functions are inverses of each other?
- What happens when you compose a function with its inverse?
- How would the graph of compare to the graph of ?
- Can every function have an inverse? Why or why not?
- How does the domain and range of a function affect its inverse?
Tip: To check if two functions are inverses, you can compose them and see if the result is the identity function: and .
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Inverse Functions
Formulas
Inverse function formula: g^{-1}(x)
g(x) = 3x - 2
g^{-1}(x) = (x + 2) / 3
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 9-11