Math Problem Statement

Use the graph of the function f to find the indicated values: f^{-1}(3), f^{-1}(4), and f^{-1}(5).

Solution

To solve for f1(3)f^{-1}(3), f1(4)f^{-1}(4), and f1(5)f^{-1}(5), we need to find the corresponding x-values on the graph where the function f(x)f(x) equals the given y-values.


(a) f1(3)f^{-1}(3):

  1. Look for y=3y = 3 on the graph.
  2. Follow horizontally to see where it intersects the function.
  3. At y=3y = 3, the graph intersects at x=2x = 2.

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


(b) f1(4)f^{-1}(4):

  1. Look for y=4y = 4 on the graph.
  2. Follow horizontally to see where it intersects the function.
  3. At y=4y = 4, the graph intersects at x=0x = 0 and x=3x = 3.

Thus, f1(4)=0f^{-1}(4) = 0 and x=3x = 3.


(c) f1(5)f^{-1}(5):

  1. Look for y=5y = 5 graphically). -( --- ; clearing..

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Math Problem Analysis

Mathematical Concepts

Functions
Inverse Functions
Graph Interpretation

Formulas

If f(x) = y, then f^{-1}(y) = x

Theorems

The definition of inverse functions: f^{-1}(y) gives the x-value where f(x) = y.

Suitable Grade Level

Grades 9-11