Math Problem Statement
Assume that the given function has an inverse function.
Given
f(3) = 2, find f −1(2).
f −1(2)
=
Solution
To find , we need to understand that is the inverse function of . This means that if , then .
Given that: This implies that:
Thus:
Would you like more details or have any further questions?
Here are 5 related questions to consider:
- What is the definition of an inverse function?
- How do you determine if a function has an inverse?
- If , what does equal?
- How would you graphically interpret the inverse function of ?
- Can every function have an inverse? If not, why?
Tip: A function has an inverse only if it is one-to-one, meaning it passes both the horizontal and vertical line tests.
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Function Notation
Formulas
f(a) = b implies f^(-1)(b) = a
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 9-12