Math Problem Statement
Evaluate g(f(6)) using the provided graphs for f(x) and g(x).
Solution
Let's solve the problem using the provided graphs for and , and the given composition .
Step 1: Evaluate
From the graph of (left-hand side):
- Locate .
- From the graph, the corresponding value of is 7.
Thus, .
Step 2: Evaluate
Now, using the graph of (right-hand side):
- Locate .
- From the graph, the corresponding value of is 0.
Thus, .
Final Answer:
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Related Questions:
- How would the solution change if were a different value, say ?
- How is the process of finding related to function composition in general?
- Can ever equal given these graphs? Why or why not?
- What is the domain of in this scenario?
- What is the range of when ?
Tip:
When evaluating composite functions graphically, carefully match the -value on one graph to the -value on the other!
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Math Problem Analysis
Mathematical Concepts
Function Composition
Graphical Interpretation of Functions
Formulas
f(a) = b (from graph of f(x))
g(b) = c (from graph of g(x))
Theorems
Definition of Function Composition
Suitable Grade Level
Grades 9-12