Sign Up

Sign Up to our MetaHub questions and Answers Engine to ask questions, answer members' questions, and connect with other teachers & members.

Have an account? Sign In


Have an account? Sign In Now

Sign In

Login to our META-HUB questions & Answers Forum

Sign Up Here


Forgot Password?

Don't have account, Sign Up Here

Forgot Password

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.


Have an account? Sign In Now

Sorry, you do not have permission to ask a question, You must login to ask a question.


Forgot Password?

Need An Account, Sign Up Here

Please briefly explain why you feel this question should be reported.

Please briefly explain why you feel this answer should be reported.

Please briefly explain why you feel this user should be reported.

Sign InSign Up

META-HUB

META-HUB Logo META-HUB Logo

META-HUB Navigation

  • Forum
  • About Us
  • Contact Us
    • Support Us
    • Sponsoring Partners
Search
Ask A Question

Mobile menu

Close
Ask a Question
  • Categories
  • Groups page
  • Badges
  • Users
  • Help
  • Forum
  • About Us
  • Contact Us
    • Support Us
    • Sponsoring Partners
Home/ Questions/Q 1504
Next
In Process

META-HUB Latest Questions

Janaka Rodrigo
  • 3
Janaka RodrigoLevel 2
Asked: February 23, 20232023-02-23T23:13:23+05:30 2023-02-23T23:13:23+05:30In: Algebra ( වීජ ගණිතය )

Composite functions

  • 3

1)What are the conditions required to be satisfied to exist the composite function f(g(x))?

2)Do we need range of g to be a subset of domain of f or is intersection of mentioned range and domain sufficient and what is the domain of f(g(x)) ?

3)For what real values of k can f(g(x)) be defined?

question
  • 4 4 Answers
  • 152 Views
  • 0 Followers
  • 0
Answer
  • Report

4 Answers

  • Voted
  • Oldest
  • Recent
  • Random
  1. Janaka Rodrigo
    Janaka Rodrigo Level 2 English medium advanced level mathematics teacher at St Benedicts College Colombo 13
    2023-02-27T15:05:48+05:30Added an answer on February 27, 2023 at 3:05 pm

    1)When f(x) and g(x) are given as expressions you can just replace x in f by g(x) and it gives an expression for f(g(x)).

    Let f(x) = x²  , g(x) =  √(x – 1)                                      f(g(x)) = x – 1 and f(g(0))= -1

    2)When domains of f and g given you can find the range of g , and f(g(x)) exists if the range of g is a subset of domain of f  . In this case domain of f(g(x)) is same as the domain of the function g.

    In the previous example if domain of f given as all real numbers and domain of g as real numbers not less than 1 ,  range of g is set of positive real numbers including 0 and it is subset of domain of f . Therefore f(g(x)) can be defined. But f(g(0)) can not be defined because 0 is not in the domain of the composite function. Since range of f is not a subset of domain of g ,  g(f(x)) can not be defined.

    3)If you are asked to find f(g(x)) with it’s domain without giving domains of f and g , you need to restrict the domain of g in order to make range of g to be a subset of domain of f.

    Let f(x) = √(x -1) , g(x) = x²                                       here you need to restrict domain of g to             (-∞ , 1] ∪  [ 1 , ∞ ) in order have range of g that is [ 1  ,  ∞ ) as a subset of domain of f.

    Hope this answer would be sufficient to get the clear picture of the issue. I think better way to get this fully understood is to practice for few more problems.  Appreciate your suggestions regarding this answer. Because of a system error sometimes your reply can be taken as another answer.

    • 0
      • Report
  2. Gaya Nayomi
    Gaya Nayomi Level 1 ( Top Rated ) Senior Lecturer-University of Sri Jayewardenepura
    2023-03-18T20:17:40+05:30Added an answer on March 18, 2023 at 8:17 pm
    This answer was edited.
    1. The answer you have provided to your own question #1 is not the answer to the question you have asked. You have explained a procedural step to find the composite function f(g(x)) (when it exists) when f(x) and g(x) are given. But your question (which is not clearly stated), we think, is about the conditions under which a composite function exists. Assuming it is “What are the conditions required for f(g(x)) to exist?”, the answer is as follows:

              Conditions for f(g(x)) to exist are,

              * the range of g(x) must be a subset of the domain of f(x)

                    Or

               *f(g(x)) must be defined with the domain of g(x) restricted so that its range is a subset of the domain of f(x).

         2. This has been already answerd in the response to #1.

         3. This question makes no sense. (what’s k?)

    ~MetaHub Panel for the Teachers’ Forum

    • 0
      • Report
    • Janaka
      Janaka
      2023-03-18T22:56:15+05:30Replied to answer on March 18, 2023 at 10:56 pm

      Thank you very much for helping to clear doubts. In 1 st case I have not mentioned functions , therefore don’t we have to treat them as just polynomial expressions? In the 3 rd case I can not see k there , could you please explain little bit more Madam?

      • 0
        • Report
      • Janaka
        Janaka
        2023-03-18T23:17:12+05:30Replied to answer on March 18, 2023 at 11:17 pm

        Really sorry for not pointing it out, that should be x instead of k Madam. Hope you may excuse me,  still I couldn’t find how to use options like editing , deleting in my android.

        • 0
          • Report

You must login to add an answer.


Forgot Password?

Need An Account, Sign Up Here

Sidebar

Ask A Question

Stats

  • Questions 74
  • Answers 94
  • Best Answers 4
  • Users 711
  • Popular
  • Answers
  • meta-hub-user2

    ප්‍රති අවකලයට අනන්තය ආදේශ කල හැකිද?

    • 5 Answers
  • Jp

    සංකීර්ණ සංඛයා සමිබන්දව

    • 5 Answers
  • Ujala123

    Functions

    • 5 Answers
  • හිරාන්
    හිරාන් added an answer කොටු දැල =12/46 රුක් සටහන= 12/49 සිද්දියෙ අවස්තා ගාණ පමණක්… December 15, 2024 at 12:12 pm
  • Bourbaki
    Bourbaki added an answer Monty hall type එකේ ප්‍රශ්න ගැන පොඩ්ඩක් හොයල බලුවොත් idea… November 9, 2024 at 12:29 am
  • Bourbaki
    Bourbaki added an answer November 4, 2024 at 7:00 pm

Related Questions

  • Rational Numbers

    • 1 Answer
  • වර්ගජ සමීකරණ

    • 0 Answers
  • Problem solving

    • 2 Answers
  • Factors

    • 2 Answers
  • Logarithmic rules

    • 0 Answers

Top Members

Gaya Nayomi

Gaya Nayomi

  • 0 Questions
  • 1k Points
Level 1 ( Top Rated )
Shelton

Shelton

  • 0 Questions
  • 1k Points
Level 1 ( Top Rated )
Janaka Rodrigo

Janaka Rodrigo

  • 22 Questions
  • 230 Points
Level 2

Trending Tags

complex numbers infinite value infinity not defined poll probability pure maths q quadratic question questions zero බිංදුවෙහි බිංදුව වෙනි බලය පිලිබද ඔබගේ අදහස කුමක්ද? සංකල්පීය වශයෙන් ඇත්ටම අර්ථ දැක්විය නොහැකිද? නැත්නම් පිළිතුර 1 වේද?

Explore

  • Categories
  • Groups page
  • Badges
  • Users
  • Help

Footer

META-HUB

Mathematics Education Teacher Awareness Hub (META Hub) is a web-based platform that connects Mathematics teachers in Sri Lanka with the field of Mathematics Education

About Us

  • Meet The Team
  • Blog
  • About Us
  • Contact Us

Legal Stuff

  • Terms of Use
  • Privacy Policy
  • Cookie Policy

Help

  • Knowledge Base
  • Support

© 2023 MetaHub. All Rights Reserved.
Web Solutions by CYBEGEN