A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2. Find g(f(x)). Show each step of your work. Help please

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

    @marihelenh can you help me with this one too?

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

    @freckles

  3. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You would replace what you have for f(x) into the x position of g(x). \[\left( 4x ^{2}+x+1 \right)^{2}-2\] Does that make sense?

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

    but where does the x^2-2 go

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

    the -2 is there but the x^2 i only see the ^2 added but not the x

  6. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The f(x) becomes a function of g(x), so you just replace what f was equal to into wherever the x is in the g equation.

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

    oh i think i get it

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

    yes i get it :D

  9. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok great! It is a little difficult trying to explain on here sometimes.

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

    4x^4+x^3-1 would this be the final answer?

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

    @marihelenh

  12. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just one sec, let me check.

  13. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No, the answer is actually even longer.

  14. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    To find the answer you would have to do, \[(4x ^{2}+x+1)(4x ^{2}+x+1) -2\]

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

    This is so hard, i thought i understood but now i don't.

  16. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you have to simplify it?

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

    It says Find g(f(x)) so I think I have to but maybe not

  18. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, if you don't have to, you already have your answer, but I will help you simplify it. Just hang in with me. It will seem confusing, but we will get through it and to the answer. OK?

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

    ok, thank you

  20. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The first thing you should do, is multiply the first term of the first set by the second set. |dw:1436743172709:dw|

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

    16x^5?

  22. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It would be 16x^4 + 4x^3 + 4x^2

  23. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Then the same thing with the second term |dw:1436743368652:dw| 4x^3 + x^2 + x

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

    4 times 4 = 16 then 16^4 times x = 16x^5 or the x doesnt add ^1?

  25. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No, it doesn't. You add the current exponents, so it would be 2 + 2 = 4.

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

    oh ok

  27. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Then you would do it with the third term. |dw:1436743540161:dw| 4x^2 + x + 1

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

    and what happens to the -2?

  29. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That will get added on in the end when we put all of the terms together.

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

    so final answer is this 16x^4 + 4x^3 + 4x^2 - 2 ?

  31. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That is how you multiply the two trinomials out, so then add them all together. \[16x ^{4}+4x ^{3}+4x ^{2}+4x ^{3}+x ^{2}+x+4x ^{2}+x+1-2\] (I added in the -2)

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

    ^that last part is so confusing

  33. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Add like terms \[16x ^{4}+8x ^{3}+9x ^{2}+2x-1\]

  34. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you understand how I got the three different terms on the pictures by multiplying them out?

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

    yes that part i understand

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

    The f(x) becomes a function of g(x) so you just replace what f was equal to into wherever the x is in the g equation. Then you get: (4x^2+x+1)^2(4x^2+x+1)^2-2 then multiply 4x^2 by all terms of second equation to get 16x^4 now multiply x by all terms of second equation to get 4x^3 repeat now with last term to get 4x^2 you get 16x^4 + 4x^3 + 4x^2 now to add the -2 you add like terms to get 16x^4 + 8x^3 + 9x^2 + 2x - 1 would this be good for the answer ?

  37. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I just put the nine different terms together and then added the -2.

  38. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you just have to explain how to get the answer?

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

    yes

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

    and get the answer too

  41. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok, well then let me just fix what you have, you were pretty close.

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

    ok

  43. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then multiply 4x^2 by all terms of second equation to get 16x^4+4x^3+4x^2 now multiply x by all terms of second equation to get 4x^3+x^2+x repeat now with last term to get 4x^2+x+1 you get 16x^4+4x^3+4x^2+4x^3+x^2+x+4x^2+x+1 now to add the -2 and add like terms to get 16x^4+8x^3+9x^2+2x-1

  44. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The first three lines were good. You just had to add a little extra into the next ones, but it was all looking good.

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

    yeah i missed a couple of things, thank you so much for your time :D

  46. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It's not a problem. I am soooo sorry for how long it took and how confusing it was.

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

    I don't care as long as I get it, thank you.

  48. marihelenh
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're welcome

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.