Math Problem Statement
f(x)=
−x−5
g, of, x, equals, x, squared, minus, 6, x, plus, 13
g(x)=
x2−6x+13
Find: , left parenthesis, f, circle, g, right parenthesis, left parenthesis, x, right parenthesis
Find: (f∘g)(x)
Solution
To find , we need to evaluate the composition of the functions and . The composition means that we substitute into the function .
Given:
To find , substitute into :
Substitute into :
Substitute :
Distribute the negative sign:
Simplify the expression:
Thus, the composition is:
Would you like more details or have any questions?
Here are 5 related questions:
- How do you find the composition of two functions in general?
- What is the domain of the composite function ?
- How does the composition of functions relate to function transformations?
- Can the order of composition affect the result, i.e., is the same as ?
- What are some practical applications of function composition in real-world problems?
Tip: When composing functions, always carefully substitute the inner function into the outer function and simplify step by step.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Algebra
Polynomial Functions
Formulas
Function Composition: (f ∘ g)(x) = f(g(x))
Theorems
Function Composition Theorem
Suitable Grade Level
Grades 9-12
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