Math Problem Statement

Using the graph, determine the value of f^{-1}(3).

Solution

To solve for f1(3)f^{-1}(3) using the graph, we need to find the value of xx such that f(x)=3f(x) = 3. In other words, find the xx-coordinate where the function ff outputs 3.

Steps to Determine f1(3)f^{-1}(3):

  1. Identify the point on the graph where y=3y = 3.
  2. Find the corresponding xx-value for that yy-coordinate.

From the graph:

  • When y=3y = 3, the corresponding xx-value is 5.

Therefore:

f1(3)=5f^{-1}(3) = 5

Final Answer:

5\boxed{5}


Would you like further clarification or additional details?

Related Questions:

  1. What is the definition of an inverse function?
  2. How do you verify that two functions are inverses of each other?
  3. What is the general process for finding f1(x)f^{-1}(x) algebraically?
  4. How can you check if a function is one-to-one (invertible) using the graph?
  5. How do you determine f1(x)f^{-1}(x) when given a table of values?

Tip:

The graph of a function and its inverse are symmetric about the line y=xy = x. This symmetry can help verify inverse relationships visually.

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Math Problem Analysis

Mathematical Concepts

Inverse Functions
Graph Analysis
Linear Functions

Formulas

Inverse function property: f^{-1}(y) = x where f(x) = y

Theorems

The graph of a function and its inverse are symmetric about the line y = x.

Suitable Grade Level

Grade 10-11