Podcast
Questions and Answers
To find the domain of a composite function, first find the domain of the ______ function.
To find the domain of a composite function, first find the domain of the ______ function.
inside
The composition of functions is denoted as (f o ______)(x).
The composition of functions is denoted as (f o ______)(x).
g
The final domain of a composite function must include the restrictions of both the inside and the ______ functions.
The final domain of a composite function must include the restrictions of both the inside and the ______ functions.
composed
For the function f(x) = √x, its domain is defined as {x | x ≥ ______}.
For the function f(x) = √x, its domain is defined as {x | x ≥ ______}.
Signup and view all the answers
The function h(x) = 1/x has a domain restriction that excludes ______.
The function h(x) = 1/x has a domain restriction that excludes ______.
Signup and view all the answers
The domain of the function m(x) = x² is {x | x ∈ ______}.
The domain of the function m(x) = x² is {x | x ∈ ______}.
Signup and view all the answers
For the composite function h(o)p (x), the output is expressed as ______ = 1/(x² - 10x + 25).
For the composite function h(o)p (x), the output is expressed as ______ = 1/(x² - 10x + 25).
Signup and view all the answers
The expression p(o)n(x) simplifies to ______ = x².
The expression p(o)n(x) simplifies to ______ = x².
Signup and view all the answers
Study Notes
Composite Function Domain
-
Steps to find the domain of a composite function:
- Find the domain of the inner function.
- Find the domain of the composed function (result).
- The final domain must include the restrictions from both the inner and composed functions.
Function Compositions
-
f(x) = √x, g(x) = √x, h(x) = 1/x
- f(g(x)) = √√x = √x - Domain: x ≥ 0
- h(f(x)) = 1/√x - Domain: x > 0
- g(f(x)) = √√x = √x - Domain: x ≥ 0
- f(h(x)) = √(1/x) - Domain: x > 0
- h(g(x)) = 1/√x - Domain: x > 0
- n(x) = x + 5
Specific Function Compositions
- p(x) = x² - 10x + 25:
- p(n(x)) = (x + 5)² - 10(x + 5) + 25 = x² - 5 +25- Domain: all real numbers
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz covers the domain of composite functions, focusing on specific function compositions such as f(x) = √x and h(x) = 1/x. You'll learn the steps to determine the domain of inner and composed functions, along with detailed examples to clarify the concepts. Test your understanding of function compositions and their respective domains.
