Math Problem Statement
Let f ( x )
2 x + 2 and g ( x )
3 x 2 + 3 x . After simplifying, ( f ∘ g ) ( x )
Solution
Given the functions:
and ,
we want to find , which means applying to the result of . This can be written as:
Step 1: Substitute into
Since , we substitute this into :
Now, using the definition of , which is , we replace in with :
Step 2: Simplify the expression
Distribute the 2:
This gives:
Thus, the simplified form of is:
Do you need further clarification or details on any step?
Here are 5 follow-up questions to consider:
- How would the result change if we switch the composition to ?
- What happens if we differentiate ?
- Can we compose more functions in a chain, like ?
- How would the composition behave for negative values of ?
- What are the general properties of function composition?
Tip: When composing functions, always substitute one function's output into the other carefully and simplify step by step.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Algebra
Polynomial Functions
Formulas
f(x) = 2x + 2
g(x) = 3x^2 + 3x
(f ∘ g)(x) = f(g(x))
Theorems
Function Composition Rule
Suitable Grade Level
Grades 9-12
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