Access over 20 million homework & study documents

Dietary guideline for americans to improve well being discussion

Content type
User Generated
Rating
Showing Page:
1/2
General Mathematics
Composition of Functions
For all values of x for which both f(ξ΅”) and g(ξ΅”) are defined, we define the following as:
󰇛
ξ΅‚  
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 󰇛
󰇛
ξ΅”
σ°‡œ
σ°‡œ
In general, the notation 󰇛
󰇛
ξ΅”
σ°‡œ
σ°‡œ, read as β€œξ΅‚ of  of ξ΅”,” means β€œξ΅‚ composed with  of ” can be
written as
󰇛
ξ΅‚  
σ°‡œσ°‡›
ξ΅”
σ°‡œ
.
Illustrative Examples:
Given the functions 
󰇛
ξ΅”
σ°‡œ
 ξ΅”
ο„Ά
 ξ₯³ and ξ΅„
󰇛
ξ΅”
σ°‡œ
 ξ΅”  ξ₯³, find the following:
a.
󰇛
  
σ°‡œσ°‡›

σ°‡œ
󰇛
  ξ΅„
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 
󰇛
ξ΅”
σ°‡œ

󰇛
  ξ΅„
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 
󰇛
ξ΅”  ξ₯³
σ°‡œ
󰇛
  ξ΅„
σ°‡œσ°‡›
ξ΅”
σ°‡œ

󰇛
ξ΅”  ξ₯³
σ°‡œ
ο„Ά
 ξ₯³
󰇛
  ξ΅„
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 ξ΅”
ο„Ά
 ξ₯΄ξ΅”  ξ₯³  ξ₯³
󰇛
  ξ΅„
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 ξ΅”
ο„Ά
 ξ₯΄ξ΅”
b.
󰇛
  
σ°‡œσ°‡›

σ°‡œ
󰇛
ξ΅„  
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 
󰇛
ξ΅”
σ°‡œ

󰇛
ξ΅„  
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 󰇛
ο„Ά
 ξ₯³σ°‡œ
󰇛
ξ΅„  
σ°‡œσ°‡›
ξ΅”
σ°‡œ

󰇛
ξ΅”
ο„Ά
 ξ₯³
σ°‡œ
 ξ₯³
󰇛
ξ΅„  
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 ξ΅”
ο„Ά
 ξ₯³  ξ₯³
󰇛
ξ΅„  
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 ξ΅”
ο„Ά
c.
󰇛
  
σ°‡œσ°‡›

σ°‡œ
󰇛
  ξ΅„
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 ξ΅”
ο„Ά
 ξ₯΄ξ΅”
󰇛
  ξ΅„
σ°‡œσ°‡›
ξ₯²
σ°‡œ
 ξ₯²
ο„Ά
 ξ₯΄σ°‡›ξ₯²σ°‡œ
󰇛
  ξ΅„
σ°‡œσ°‡›
ξ₯²
σ°‡œ
 ξ₯²
Alternative Solution:
󰇛
  ξ΅„
σ°‡œσ°‡›
ξ₯²
σ°‡œ
 󰇛
󰇛
ξ₯²
σ°‡œ
σ°‡œ
ξ΅„
󰇛
ξ₯²
σ°‡œ
 ξ₯²  ξ₯³
ξ΅„
󰇛
ξ₯²
σ°‡œ
 ξ₯³

󰇛
ξ₯²
σ°‡œ
  
󰇛
ξ₯³
σ°‡œ

󰇛
ξ₯³
σ°‡œ
 󰇛ξ₯³σ°‡œ
ο„Ά
 ξ₯³

󰇛
ξ₯³
σ°‡œ
 ξ₯²
󰇛
  ξ΅„
σ°‡œσ°‡›
ξ₯²
σ°‡œ
 ξ₯²
d.
󰇛
  
σ°‡œσ°‡›
ο†οƒš
σ°‡œ
󰇛
ξ΅„  
σ°‡œσ°‡›
ξ΅”
σ°‡œ
 ξ΅”
ο„Ά
󰇛
ξ΅„  
σ°‡œσ°‡›
ξ₯³
σ°‡œ
 󰇛ξ₯³σ°‡œ
ο„Ά
󰇛
ξ΅„  
σ°‡œ
󰇛ξ₯³σ°‡œ  ξ₯³
e.
󰇛
  
σ°‡œσ°‡›
ξ΅”
σ°‡œ

Sign up to view the full document!

lock_open Sign Up
Showing Page:
2/2

Sign up to view the full document!

lock_open Sign Up
Unformatted Attachment Preview
General Mathematics Composition of Functions For all values of x for which both f(π‘₯) and g(π‘₯) are defined, we define the following as: (𝑓 ∘ 𝑔)(π‘₯) = 𝑓(𝑔(π‘₯)) In general, the notation 𝑓(𝑔(π‘₯)), read as β€œπ‘“ of 𝑔 of π‘₯,” means β€œπ‘“ composed with 𝑔 of π‘₯” can be written as (𝑓 ∘ 𝑔)(π‘₯). Illustrative Examples: Given the functions 𝑔(π‘₯) = π‘₯ 2 βˆ’ 1 and β„Ž(π‘₯) = π‘₯ + 1, find the following: a. (π’ˆ ∘ 𝒉)(𝒙) (𝑔 ∘ β„Ž)(π‘₯) = 𝑔(β„Ž(π‘₯)) (𝑔 ∘ β„Ž)(π‘₯) = 𝑔(π‘₯ + 1) (𝑔 ∘ β„Ž)(π‘₯) = (π‘₯ + 1)2 ? ...
Purchase document to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Anonymous
Very useful material for studying!

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4