Math Problem Statement
Solution
Let's analyze the graphs and evaluate each of the expressions step-by-step.
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For :
- First, find on the graph of . When , .
- Next, use on the graph of . When , .
- So, .
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For :
- First, find on the graph of . We already know from the previous step that .
- Next, use on the graph of . When , .
- Thus, .
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For :
- First, find on the graph of . When , .
- Next, use on the graph of . When , .
- Therefore, .
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For :
- First, find on the graph of . When , .
- Next, use on the graph of . When , .
- So, .
Final Answers:
Would you like further details on any of these steps?
Here are some related questions for additional practice:
- What is ?
- What is ?
- What is ?
- What is ?
- How would you find ?
Tip: For composite functions like , evaluate the inner function first, then use its result to find the value of the outer function.
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Math Problem Analysis
Mathematical Concepts
Composite Functions
Function Evaluation
Graphs of Functions
Formulas
f(g(x)): Evaluate g(x) first, then f(result)
g(f(x)): Evaluate f(x) first, then g(result)
Theorems
Function Composition
Suitable Grade Level
Grades 9-12
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