Comparing the domains of composite functions

Thread starter srfriggen
Start date Sep 19, 2020
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Composite domains Functions

In summary, a composite function is a combination of two or more functions where the output of one function is used as the input for another. To compare the domains of composite functions, one must first find the domains of each individual function and then check for compatibility. This is important to ensure the composite function is well-defined and can be evaluated for all possible inputs. Common methods for comparing domains include graphing, algebraic methods, and visual aids. In real-life situations, comparing domains of composite functions is useful in fields such as engineering and economics to model and analyze complex systems.

Sep 19, 2020

srfriggen

Homework Statement: The problem and solution are posted in an attachment.

Relevant Equations: h(x) = f(g(x)) and more are in attachment.

Hello,

I have attached my question and the work. I believe the answer is correct. Looking for verification.

Thank you!

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Sep 19, 2020

PeroK

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Must be easier with Latex, but correct.

1. What are composite functions?

Composite functions are functions that are formed by combining two or more functions. The output of one function becomes the input of the other function.

2. How do you compare the domains of composite functions?

To compare the domains of composite functions, you need to find the common values in the domains of the individual functions. The domain of the composite function will be the set of all common values.

3. What is the importance of comparing the domains of composite functions?

Comparing the domains of composite functions is important because it helps us understand the restrictions on the inputs of the composite function. It also allows us to determine the range of the composite function.

4. Can the domain of a composite function be different from the domains of its individual functions?

Yes, the domain of a composite function can be different from the domains of its individual functions. This can happen when the individual functions have different domains, but their intersection is not empty.

5. How can we represent the domain of a composite function?

The domain of a composite function can be represented in set notation or interval notation. For example, if the domain is the set of real numbers greater than 0, it can be represented as (0, ∞) in interval notation or {x | x > 0} in set notation.