Math Problem Statement
Solution
Let's evaluate the expressions using the table provided.
Given:
- x values:
- f(x) values:
- g(x) values:
The questions involve compositions of functions, which follow the rule:
Now, let's solve the expressions step-by-step.
a.
- Find : From the table, .
- Now, find : From the table, .
- So, .
b.
- Find : From the table, .
- Now, find : From the table, .
- So, .
c.
- Find : From the table, .
- Now, find : From the table, .
- So, .
d.
- Find : From the table, .
- Now, find : From the table, .
- So, .
e.
- Find : From the table, .
- Now, find : From the table, .
- So, .
f.
- Find : From the table, .
- Now, find : From the table, .
- So, .
Final Answers:
a.
b.
c.
d.
e.
f.
Would you like to explore any of these steps further?
5 Related Questions:
- How do you identify the domain and range of a function?
- What is the difference between and ?
- How do you compose more than two functions, like ?
- What is the significance of function composition in real-world applications?
- How can we verify if a function is invertible through composition?
Tip:
When working with function compositions, always solve the inner function first before moving to the outer function.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Algebra
Formulas
(f ∘ g)(x) = f(g(x))
(g ∘ f)(x) = g(f(x))
Theorems
Function Composition
Suitable Grade Level
Grades 9-11
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