Math Problem Statement

What is the value of f^(-1)(3) based on the given function table?

Solution

To solve the problem in the uploaded image:

We are tasked with finding f1(3)f^{-1}(3). This means we are looking for the value of xx such that f(x)=3f(x) = 3.

From the table:

  • f(x)=3f(x) = 3 corresponds to x=12x = 12.

Thus, f1(3)=12f^{-1}(3) = 12.

The correct answer is 12.

Would you like further details or have any other questions?

Here are five related questions for practice:

  1. What is the value of f1(1)f^{-1}(1) based on the table?
  2. What is f1(0.75)f^{-1}(0.75)?
  3. Explain the process of finding inverse values from a function table.
  4. How do you determine if a function has an inverse that is also a function?
  5. What does it mean graphically for a function and its inverse?

Tip: For a function f(x)f(x), the inverse f1(x)f^{-1}(x) swaps the roles of xx and f(x)f(x). This means f(a)=bf(a) = b implies f1(b)=af^{-1}(b) = a.

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Math Problem Analysis

Mathematical Concepts

Inverse Functions
Function Tables

Formulas

f(a) = b implies f^(-1)(b) = a

Theorems

Properties of Inverse Functions

Suitable Grade Level

Grades 9-11