Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mitchelsewbaran

  • one year ago

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = x^3 + 4 and g(x) = cube root of (x-4)

  • This Question is Closed
  1. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, first try f(g(x)), this means put the result of function g in function f:\[f(g(x))=\left( \sqrt[3]{x-4} \right)^3+4=...\]Can you see what the next step is?

  2. mitchelsewbaran
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no. :(

  3. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What is the definition of the 3rd root of a number?

  4. mitchelsewbaran
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The number whose cube is equal to a given number

  5. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    OK, but not only a given number, but the number from which you wanted to know the 3rd root: e.g: the 3rd root of 8 is 2, because: 2^3=8. So: the 3rd root of x-4 is p, then p³=x-4. So...\[(\sqrt[3]{x-4})^3=x-4\]by definition.

  6. mitchelsewbaran
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so that will get the expression out from under the radical

  7. mitchelsewbaran
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so i'll get x-4+4

  8. mitchelsewbaran
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or x-8

  9. mitchelsewbaran
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @ZeHanz am i correct?

  10. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You get x-4+4=x in my book...

  11. mitchelsewbaran
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh srry

  12. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So we've done the first half of the proof. Now the second: put the result of f in g:\[g(f(x))=\sqrt[3]{x^3+4-4}\]

  13. mitchelsewbaran
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok. thnx. but where did u get p from?

  14. ZeHanz
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    p is not important. You can name it anyway you want. Just look at it this way: say you've got a terribly complex expression, such as:\[3x^{23}-5x^{16}+\frac{ 1 }{ 2x }\] First, they want you to calculate the 3rd root of it. I really don't know what it would be, so let's call it p for now:\[p=\sqrt[3]{3x^{23}-5x^{16}+\frac{ 1 }{ 2x }}\]Looks awful, not? Now you have to calculate .... p³. Well, you don't have to think long about it, youve got your original complex expression back! The reason for this, that the 3rd root and the 3rd power are each other's inverse. This means: they undo each other's effect on numbers you put in!

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

    • 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.