Math Problem Statement

Evaluate f(g(3)) using the given graphs of f and g.

Solution

You are asked to evaluate f(g(3))f(g(3)) using the graphs of functions ff and gg.

Step-by-step process:

  1. Find g(3)g(3) from the graph of gg:

    • Locate x=3x = 3 on the graph of gg.
    • From the graph, at x=3x = 3, g(3)=2g(3) = 2 (since the point on the graph corresponding to x=3x = 3 is (3,2)(3, 2)).
  2. Now, find f(g(3))=f(2)f(g(3)) = f(2) from the graph of ff:

    • Using g(3)=2g(3) = 2, now locate x=2x = 2 on the graph of ff.
    • From the graph, at x=2x = 2, f(2)=5f(2) = 5 (since the point on the graph corresponding to x=2x = 2 is (2,5)(2, 5)).

Thus, f(g(3))=5f(g(3)) = 5.

Would you like more details or have any questions about this problem?

Here are some related questions for further practice:

  1. What is f(g(1))f(g(1)) based on the graphs provided?
  2. Find f(g(4))f(g(4)) using the graphs.
  3. What is g(f(3))g(f(3)) using the graphs?
  4. Determine the value of g(g(5))g(g(5)).
  5. What would f(f(2))f(f(2)) be from the graphs?

Tip: For compositions of functions, always work from the innermost function outward!

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Math Problem Analysis

Mathematical Concepts

Function Composition
Graph Reading

Formulas

f(g(x))

Theorems

Composition of Functions

Suitable Grade Level

Grades 9-12