Math Problem Statement
find inverse of the function f(x)=x^5-3 over 2
Solution
To find the inverse of the function , follow these steps:
Step 1: Express the function in terms of
Let .
So,
Step 2: Solve for
Now, we need to solve for in terms of .
First, multiply both sides by 2 to eliminate the fraction:
Next, add 3 to both sides:
Finally, take the 5th root of both sides:
Step 3: Write the inverse function
The inverse of the function is:
Step 4: Substitute back to
If you want to express the inverse as a function of , replace with :
Thus, the inverse of is:
Would you like more details or have any questions?
Here are 5 related questions to explore:
- How do you verify if a function has an inverse?
- What are the domain and range of ?
- How do you prove that ?
- What happens if you apply transformations to the function ?
- How do you find the derivative of ?
Tip: Inverse functions "undo" the operations of the original function.
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Algebraic Manipulation
Radical Equations
Formulas
f^{-1}(x) = \sqrt[5]{2x + 3}
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 10-12