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anonymous

  • one year ago

Let f(x) = -2x - 7 and g(x) = -4x + 3. Find (f o g)(-5)

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  1. jim_thompson5910
    • one year ago
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    (f o g)(-5) is the same as f(g(-5)) the first task is to find g(-5). Do you know how to do this?

  2. anonymous
    • one year ago
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    A. -53 C.23 D.3

  3. anonymous
    • one year ago
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    No i have no clue

  4. anonymous
    • one year ago
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    @satellite73

  5. anonymous
    • one year ago
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    Could you help @jim_thompson5910

  6. anonymous
    • one year ago
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    @SolomonZelman

  7. jim_thompson5910
    • one year ago
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    g(x) = -4x + 3 g(-5) = -4(-5) + 3 ... replace every x with -5 g(-5) = ??

  8. misssunshinexxoxo
    • one year ago
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    On OS we help people learn; Jim is trying to make sure you are understanding this

  9. anonymous
    • one year ago
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    Oh i know and i defiantly want the help

  10. UsukiDoll
    • one year ago
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    (f o g)(-5) well first let's do (f o g ) which means that the g(x) equation is placed inside the f(x) equation

  11. anonymous
    • one year ago
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    20+3

  12. UsukiDoll
    • one year ago
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    whoa... let's do this step by step

  13. anonymous
    • one year ago
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    Oh sorry i was replying to what @jim_thompson5910 started

  14. jim_thompson5910
    • one year ago
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    so you should find that g(-5) = 23 agreed?

  15. anonymous
    • one year ago
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    correct

  16. jim_thompson5910
    • one year ago
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    f(g(-5)) becomes f(23) after you replace g(-5) with 23

  17. jim_thompson5910
    • one year ago
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    now follow the same basic steps to calculate f(23)

  18. UsukiDoll
    • one year ago
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    ok it's ok didn't see that :) anyway given the functions f(x) = -2x-7 and g(x) = -4x+3 we need to place g(x) =-4x+3 into the f(x) so for every x in f(x) the g(x) takes it's place

  19. UsukiDoll
    • one year ago
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    so the end result should be -2(insert g(x) function here)-7

  20. UsukiDoll
    • one year ago
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    then combine like terms and evaluate when x = -5

  21. anonymous
    • one year ago
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    im lost

  22. anonymous
    • one year ago
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    Is the answer 23?

  23. jim_thompson5910
    • one year ago
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    no

  24. UsukiDoll
    • one year ago
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    I agree with jim there's more to be done...

  25. anonymous
    • one year ago
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    ok im ready to learn the rest

  26. UsukiDoll
    • one year ago
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    k.. so did you already place your g(x) into your entire f(x) function?

  27. anonymous
    • one year ago
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    No i got lost after we got f(23)

  28. jim_thompson5910
    • one year ago
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    To calculate f(23), replace every x in f(x) with 23 f(x) = -2x - 7 f(23) = -2*23 - 7 f(23) = ??

  29. UsukiDoll
    • one year ago
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    that means x = 23 evaluate the f(x) function

  30. jim_thompson5910
    • one year ago
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    it's just like the g(x) one

  31. anonymous
    • one year ago
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    -46

  32. anonymous
    • one year ago
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    f(23)=-46-7

  33. jim_thompson5910
    • one year ago
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    keep going

  34. UsukiDoll
    • one year ago
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    almost there

  35. anonymous
    • one year ago
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    46-7=39

  36. UsukiDoll
    • one year ago
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    we have two negative numbers so the negative numbers are supposed to increase, not decrease

  37. anonymous
    • one year ago
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    opps wrong

  38. anonymous
    • one year ago
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    -53

  39. UsukiDoll
    • one year ago
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    yes!

  40. jim_thompson5910
    • one year ago
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    good

  41. UsukiDoll
    • one year ago
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    do you want to see another method of solving this equation as a reference?

  42. anonymous
    • one year ago
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    yay we did it

  43. anonymous
    • one year ago
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    yes that would be great

  44. UsukiDoll
    • one year ago
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    ok so here's how I would tackle this problem (f o g ) (-5) first I will tackle f o g portion and then evaluate when x = -5 so f o g means that we place our g(x) function inside all x's of the f(x) function f(x) = -2x-7 and g(x) = -4x+3 f o g -2(-4x+3)-7 distribute the -2 8x-6-7 8x-13 so our f o g = 8x-13 now evaluating when x = -5 f o g (-5) = 8(-5)-13 = -40-13 = -53

  45. anonymous
    • one year ago
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    Can you guys help me solve another @UsukiDoll @jim_thompson5910

  46. UsukiDoll
    • one year ago
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    sure

  47. anonymous
    • one year ago
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    Let f(x) = x + 2 and g(x) = x2 Find ( g o f)(-5)

  48. UsukiDoll
    • one year ago
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    \[\large f(x) = x+2, g(x) = x^2 \]

  49. UsukiDoll
    • one year ago
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    this is similar to the previous problem. while our x still remains the same g o f means that we place our entire f(x) function inside the x's of the g(x) function so g o f = (insert f(x) here)^2

  50. anonymous
    • one year ago
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    so is x -2?

  51. UsukiDoll
    • one year ago
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    our f(x) = x+2 and we need place it inside g(x). Since g(x) =x^2 g o f = (f(x) function)^2

  52. anonymous
    • one year ago
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    so X^2+X+2?

  53. UsukiDoll
    • one year ago
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    \[g o f =(x+2)^2 \] that second power means write (x+2) two times after that, we need to use FOIL to expand

  54. anonymous
    • one year ago
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    your gonna have to hold my hand on this one cuz im totally lost lol im sorry

  55. UsukiDoll
    • one year ago
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    alirght.. so we write (x+2) two times (x+2)^2 means (x+2)(x+2) now using FOIL (x)(x)+2(x)+2(x)+(2)(2) so what's 2 x 2 2x + 2x and x times x I guess that's the closest way of notating multiplication

  56. anonymous
    • one year ago
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    Ok so where do we go from this?

  57. UsukiDoll
    • one year ago
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    first tell me what 2 x 2 is then tell me what 2x+2x is .. I will factor out the x to make it easier x(2+2)

  58. anonymous
    • one year ago
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    2x2=4

  59. anonymous
    • one year ago
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    2x+2x=4X

  60. UsukiDoll
    • one year ago
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    mhm last one what is (x)(x) . I'll make this easier by rewriting it and using the addition exponential rule, \[\large (x)(x) \rightarrow x^1x^1 \rightarrow x^{1+1}\] so you just have to solve for the exponent part. what is 1+ 1

  61. anonymous
    • one year ago
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    2

  62. anonymous
    • one year ago
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    \[x ^{2}\]

  63. UsukiDoll
    • one year ago
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    yes so now we have \[g o f =x^2+4x+4 \]

  64. UsukiDoll
    • one year ago
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    so now we evaluate this when x = -5. so replace all x's with -5

  65. anonymous
    • one year ago
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    25-20+4=9

  66. UsukiDoll
    • one year ago
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    \[g o f (-5) =(-5)^2+4(-5)+4\] \[g o f (-5) =25-20+4 \rightarrow 5+4 = 9 \] correct

  67. anonymous
    • one year ago
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    Thank you very much

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