6 Questions
What is the result of the operation of two functions?
A new function
What happens when a function is composed with another function?
The result is a new function
In function operations, what is the role of the domain and codomain?
Defining the input and output of the functions
What is the result of adding two functions f(x) and g(x)?
f(x) + g(x)
What is the result of subtracting two functions f(x) and g(x)?
f(x) - g(x)
What is the result of composing two functions f(x) and g(x)?
f(g(x))
Study Notes
Function Operations
- When two functions are added or subtracted, the result is a new function that takes the sum or difference of the outputs of the original functions.
- The domain of the resulting function is the intersection of the domains of the original functions, and the codomain is the set of all possible sums or differences of the codomains of the original functions.
Function Composition
- When two functions are composed, the output of one function becomes the input of the other function.
- The resulting function is a new function that takes the output of the first function as its input, and applies the second function to produce the final output.
- The domain of the resulting function is the domain of the first function, and the codomain is the codomain of the second function.
Result of Function Composition
- The result of composing two functions f(x) and g(x) is a new function h(x) = g(f(x)), where the output of f(x) becomes the input of g(x).
Explore the operations of functions in this quiz. Discover the result of combining two functions, the impact of composing functions, and the significance of domain and codomain in function operations. Test your knowledge and understanding of these fundamental concepts in mathematics.
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