Math Problem Statement
Find a formula for the inverse of the following function, if possible.
g(x)=x^1/3−1
Solution
The function given is:
To find the inverse function , follow these steps:
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Replace with :
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Solve for in terms of :
Now cube both sides to eliminate the cube root:
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Express in terms of :
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Replace with to get the inverse function**:
Thus, the inverse of the function is:
Do you have any questions about this solution, or would you like more details?
Here are five related questions:
- How can you verify that two functions are inverses of each other?
- What is the domain and range of the function ?
- How does the process of finding the inverse differ for non-linear functions?
- What happens if a function doesn't have an inverse? How do you check?
- What are some practical applications of inverse functions?
Tip: To check if your inverse is correct, compose the original function with the inverse and . Both should give you .
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Math Problem Analysis
Mathematical Concepts
Algebra
Inverse Functions
Cube Roots
Formulas
Inverse function formula g^{-1}(x)
Cube root property
Theorems
Inverse Function Theorem
Properties of Cube Roots
Suitable Grade Level
Grades 10-12