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anonymous

  • one year ago

f(x) = 6x2 - x - 12 and g(x) = 2x - 3 find the function (f/g)(x)

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  1. UsukiDoll
    • one year ago
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    \[f(x) = 6x^2-x-12\] \[g(x) = 2x-3 \] If your question is just asking to find the function \[\frac{f(x)}{g(x)}\] then we just place the f(x) here ------------------ place the g(x) here the notation I'm using is the same as (f/g)(x)

  2. anonymous
    • one year ago
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    But I can't simplify 6x^2 - x -12. So there is no real answer for this equation?

  3. UsukiDoll
    • one year ago
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    we could try to simplify 6^x-x-12 using b^2-4ac which is the discriminant.

  4. UsukiDoll
    • one year ago
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    (-1)^2-4(6)(-12) for a = 6, b = -1, and c = -12

  5. UsukiDoll
    • one year ago
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    if we have a perfect square number like 25 16 9 then we can factor if we have a non-perfect square number like 3 -32... then we can't factor and have to use the quadratic equation (or just leave the problem alone in this case)

  6. UsukiDoll
    • one year ago
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    so from the discriminant (-1)^2-4(6)(-12) = 1-24(-12) =1+288 =289 we have a perfect square .. because the square root of 289 is 17

  7. UsukiDoll
    • one year ago
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    so we can factor 6x^2-x-12... it becomes (2x-3)(3x+4)

  8. anonymous
    • one year ago
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    Oh okay. so then the 2x -3 crosses each other out which leaves 3x+4?

  9. UsukiDoll
    • one year ago
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    yes! that's right! the 2x-3 terms cancels out

  10. UsukiDoll
    • one year ago
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    \[\frac{(2x-3)(3x+4)}{2x-3} \rightarrow 3x+4 \]

  11. anonymous
    • one year ago
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    Okay so if the question is Given f(x) = x + 2 and g(x) = x2 - 4, find the function (fg)(x) then the answer would be x^3 -2x^2- 4x - 8

  12. anonymous
    • one year ago
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    Or did I do that wrong? Sorry. Still trying to get the hang of this

  13. UsukiDoll
    • one year ago
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    so (fg(x) or f(x)(g(x)) means that we multiply the f(x) function with the g(x) function

  14. UsukiDoll
    • one year ago
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    f(x)(g(x) = \[(x+2)(x^2-4) \] then we use foil method

  15. UsukiDoll
    • one year ago
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    \[x^3-4x+2x^2-8\]

  16. UsukiDoll
    • one year ago
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    you've done it right....it's just that my terms have been rearranged. It means the same thing

  17. anonymous
    • one year ago
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    Okay got it! Thank you so much

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