Math Problem Statement
Composite f(g(x)) g=x-5 f=x^2+3
Solution
To find the composite function , we substitute into .
Given:
Now, for the composite function , substitute into :
Since , replace in with :
Now, expand :
Thus:
So, the composite function is:
Would you like more details or have any questions about this process?
Here are 5 related questions to expand this topic:
- How do you find the composite function if and are different?
- What is the domain of the composite function ?
- How would the composite function change if ?
- What is the difference between and ?
- How does the order of composition affect the resulting function?
Tip: Always check if the functions are defined for all in the domain before composing them.
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Math Problem Analysis
Mathematical Concepts
Algebra
Composite Functions
Quadratic Equations
Formulas
f(g(x)) = (x - 5)^2 + 3
(x - 5)^2 = x^2 - 10x + 25
Theorems
Composite Function Theorem
Quadratic Expansion
Suitable Grade Level
Grades 9-12
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