Math Problem Statement
If f(x) = 26 + 3
x + 13 and g(x) = 2x2 + 5, compute the composition (f ∘ g)(3).
(f ∘ g)(3)
Solution
To compute the composition , we need to evaluate first and then use that result as the input for .
Step 1: Compute
Given , we can substitute :
Calculate :
So,
Step 2: Compute
Given , substitute :
Simplify the expression:
Conclusion
Thus, the value of the composition is:
Would you like further details or have any questions?
Here are some related questions you might be interested in:
- 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 real-world applications?
- Can a composite function ever be undefined?
- What are some properties of composite functions?
Tip: When working with compositions of functions, always evaluate from the innermost function outward.
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Math Problem Analysis
Mathematical Concepts
Composition of functions
Quadratic equations
Fractional expressions
Formulas
Composition of functions formula
Quadratic equation formula
Theorems
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Suitable Grade Level
High school
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