Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mukushla

  • 2 years ago

Range of\[f(x)=\sqrt[3]{x-1}+\sqrt[3]{3-x}\]

  • This Question is Closed
  1. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ????

  2. akitav
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    made a stupid error, just a sec.

  3. akitav
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1347772271638:dw|

  4. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah range is limited...i dont how to evaluate the exact interval for range :(

  5. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    *know

  6. akitav
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Can you plot the two parts of the function? then combine them.|dw:1347772792991:dw| For analyzing the final result : If it's a diagonal line then yes both will go from -infinity to +infinity, IF HOWEVER it is a VERTICAL or HORIZONTAL line then your domain or range will be limited.

  7. mukushla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i want to show it algebrically if its possible !!

  8. artofspeed
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    idea: seperate f(x) into 2 functions, find the domain of the inverse of each one of the function, find the intersection of the 2 domains, that gives the range of f(x)

  9. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Range is ]0,2]. f(x) is symmetrical about x=2. I evaluated the first and second derivatives. for x<1<2 f'(x)>0 and f''(x)>0 for x<1, f'(x)>0 and f''(x)<0. behavior on other side of 2 is symmetrical. Also, evaluating the limit at -infinity, we get 0. So the graph would be something like this.|dw:1347780606499:dw| That's it. Correct me if I'm wrong.

  10. nipunmalhotra93
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Another small test is that f(x) can't be <0 because solving it gives -1<-3 which is a contradiction.

  11. harsh314
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the range of f(x) is ( 0,2]

  12. harsh314
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    to show it algebrically you need to assume \[\sqrt[3]{x-1}= \alpha\] \[\sqrt[3]{3-x}= \beta\] and after that you can obtain the required equations

  13. harsh314
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    as \[f(x)=y=\alpha +\beta\] so find out x in form of y and you would get the answer if you want more detailed solution then i can provide you that too

  14. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.