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anonymous

  • one year ago

Hi I'm new to open study, If someone could please help me with these 3 questions. I cant seem to get them right. 1) Given the following functions f(x) and g(x), solve for (f ⋅ g)(2) : f(x) = 3x2 + 2 g(x) = x − 8 2) Given the following functions f(x) and g(x), solve f[g(10)] f(x) = 10x + 8 g(x) = x + 9 3) Given the following functions f(x) and g(x), solve (f + g)(3) f(x) = 2x + 21 g(x) = x − 24

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  1. phi
    • one year ago
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    (f ⋅ g)(2) is short for f(2) * g(2) can you find f(2) ?

  2. anonymous
    • one year ago
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    I have no idea how to start.

  3. phi
    • one year ago
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    they give you a formula f(x) = 3x^2 + 2 f(x) is the "short name" and 3x^2 + 2 is the formula f(2) means: find the formula, find the "x" in the formula and replace the x with a 2 can you do that?

  4. anonymous
    • one year ago
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    So 3(2)^2+2?

  5. anonymous
    • one year ago
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    38?

  6. phi
    • one year ago
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    yes. now simplify that

  7. anonymous
    • one year ago
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    Is it 38?

  8. phi
    • one year ago
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    no. how did you get that? remember order of operations first do exponents, so first do 2^2

  9. phi
    • one year ago
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    2^2 means 2*2

  10. anonymous
    • one year ago
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    Well I replaced the x with 2. And the formula is 3x^2 + 2. Is it 16?

  11. anonymous
    • one year ago
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    3 times 4 is 12 and 12 plus 2 is 14. Sorry 14?

  12. phi
    • one year ago
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    it is worth knowing how to do this. 3*2^2 +2 first do 2^2 which is 2*2 . you get 4 so you have 3*4 +2 12+2 14 yes 14

  13. phi
    • one year ago
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    (f ⋅ g)(2) is short for f(2) * g(2) so far we have f(2) is 14 now we need g(2) can you do that ?

  14. anonymous
    • one year ago
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    Where do I start?

  15. phi
    • one year ago
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    to find g(2) find the formula for g replace any x's in the formula with 2 simplify

  16. anonymous
    • one year ago
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    How do I find the formula for g?

  17. anonymous
    • one year ago
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    Oh they gave me the formula

  18. anonymous
    • one year ago
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    g(x) = x − 8

  19. phi
    • one year ago
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    they give it to you. g(x) is the "name" they give to x-8 that is what g(x) = x − 8 means

  20. anonymous
    • one year ago
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    So g(2)=2-8

  21. phi
    • one year ago
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    yes, and that simplifies to what?

  22. anonymous
    • one year ago
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    g(2)=-6

  23. phi
    • one year ago
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    ok now we have (f ⋅ g)(2) is short for f(2) * g(2) so far we have f(2) is 14 and g(2) is -6 now we multiply to get the final answer

  24. anonymous
    • one year ago
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    14*-6=-84

  25. phi
    • one year ago
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    yes.

  26. anonymous
    • one year ago
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    Thankyou! Can you help with the other 2?

  27. phi
    • one year ago
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    Let's skip to Q3 (f + g)(3) f(x) = 2x + 21 g(x) = x − 24 can you guess what (f+g)(3) is short for ? (based on the first question)

  28. anonymous
    • one year ago
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    f(3) and g(3)

  29. phi
    • one year ago
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    it would be better to say f(3) + g(3)

  30. anonymous
    • one year ago
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    f(3)=2(3)+21 f(3)=27?

  31. phi
    • one year ago
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    yes

  32. anonymous
    • one year ago
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    So g(x) = x − 24 g(3)=3-24 g(3)= -21?

  33. phi
    • one year ago
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    yes

  34. anonymous
    • one year ago
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    And 27*-21 is -567

  35. phi
    • one year ago
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    ok, but we are doing (f + g)(3) = f(3) + g(3)

  36. anonymous
    • one year ago
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    Ok so what do we do know that we know what f and g are?

  37. phi
    • one year ago
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    the + means add

  38. anonymous
    • one year ago
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    27+(-21)=6

  39. phi
    • one year ago
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    yes. notice in Q1 we have multiply (that is what the dot means) and in this question we are adding we might also see (f-g)(3) (subtract) or (f/g)(3) divide

  40. phi
    • one year ago
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    now Q2 this one is a bit different. The formulas are not combined using add or multiply we have something called "composition" (they have to call it something)

  41. anonymous
    • one year ago
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    Im still stuck on 3

  42. anonymous
    • one year ago
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    My answer choices are: 98 198 190 2052

  43. phi
    • one year ago
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    those are the choices for (f + g)(3) where f(x) = 2x + 21 g(x) = x − 24 ??

  44. anonymous
    • one year ago
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    Yes

  45. phi
    • one year ago
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    those look like the choices for Q2 which we have not done yet

  46. anonymous
    • one year ago
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    Oh Im sorry I got confused

  47. anonymous
    • one year ago
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    The answer was 6 sorry

  48. anonymous
    • one year ago
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    Ok we can do #3 now

  49. phi
    • one year ago
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    Q2 solve f[g(10)] f(x) = 10x + 8 g(x) = x + 9 think of g(10) as some number (which it is) let's find g(10) can you do that ?

  50. anonymous
    • one year ago
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    Ok so g(10)=10+9?

  51. phi
    • one year ago
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    yes, and that simplifies to 19 so g(10) is 19 if we replace g(10) with 19 in f[g(10)] we get f(19) (the [ vs ( is just to make it easier to read in f[g(10)] ... but it means the same as parens) anyway we have figured out that f[g(10)] is the same as f(19) now we need to find f(19)

  52. anonymous
    • one year ago
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    f(x) = 10x + 8 So f(19)=10(19)+8?

  53. phi
    • one year ago
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    ok, and what number do you get?

  54. phi
    • one year ago
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    you do 10 times 19 then add 8

  55. anonymous
    • one year ago
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    198?

  56. anonymous
    • one year ago
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    Thankyou so so much. I got a 100%! I havent gotten a 100% before. You're a really good tutor!

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