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 f1(2)f^{-1}(2), we need to understand that f1(x)f^{-1}(x) is the inverse function of f(x)f(x). This means that if f(a)=bf(a) = b, then f1(b)=af^{-1}(b) = a.

Given that: f(3)=2f(3) = 2 This implies that: f1(2)=3f^{-1}(2) = 3

Thus: f1(2)=3f^{-1}(2) = 3

Would you like more details or have any further questions?

Here are 5 related questions to consider:

  1. What is the definition of an inverse function?
  2. How do you determine if a function has an inverse?
  3. If f1(b)=af^{-1}(b) = a, what does f(a)f(a) equal?
  4. How would you graphically interpret the inverse function of f(x)f(x)?
  5. 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