Math Problem Statement
Solution
The problem asks to find , which is the composition of the functions and , evaluated at . Here's how to solve this:
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Interpret the composition: This means we first need to find , and then substitute that result into the function .
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Find : From the graph, is represented by the black curve. When , locate the corresponding -value on the black curve.
By observing the black curve at , the -coordinate appears to be approximately .
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Find : Now, substitute into . The function is represented by the blue curve. Look for the -value when on the blue curve.
From the graph, when on the blue curve, the -value appears to be approximately .
Thus, .
Would you like any more details or have questions on this process?
Here are 5 related questions for further practice:
- What is using the same graph?
- Can you find ?
- What is the value of ?
- At what -value does ?
- For what value of is ?
Tip: When evaluating a composite function from a graph, it's important to track the input-output flow of values carefully, first through one function and then the next.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Graph Interpretation
Formulas
(f ∘ g)(x) = f(g(x))
Theorems
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Suitable Grade Level
Grades 9-12
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