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Adi3

  • one year ago

Will Medal!!! Please help Suppose f(x) = 3x+1 and g(x) = x^2 +2x. Find x such that f(g(x)) = 10.

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  1. Adi3
    • one year ago
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    @ganeshie8

  2. anonymous
    • one year ago
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    Use Wolfram alpha for this

  3. Adi3
    • one year ago
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    wolfram alpha is not correct

  4. DanJS
    • one year ago
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    replace each x value in f(x) with the entire function g(x)

  5. DanJS
    • one year ago
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    f(x) = 3x+1 f(g(x)) = 3*g(x) + 1

  6. Adi3
    • one year ago
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    What do you mean by that?

  7. DanJS
    • one year ago
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    g(x) = x^2+2x f(g(x)) = 3*g(x) + 1 = 3 * (x^2 + 2x) + 1

  8. DanJS
    • one year ago
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    see that

  9. Adi3
    • one year ago
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    yeah i get it

  10. DanJS
    • one year ago
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    then they tell you that equals to a value and find x

  11. Adi3
    • one year ago
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    it equals 3x^2 + 6x + 1 right

  12. DanJS
    • one year ago
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    10 = 3x^2 + 6x + 1

  13. DanJS
    • one year ago
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    yeah the f(g(x)) does, then they tell you that is equal to 10

  14. Adi3
    • one year ago
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    then how do you solve it after that, that s the part which is the most confusing for me

  15. DanJS
    • one year ago
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    it is a quadratic, to get the solution, you put it in standard form first.. ax^2+bx+c=0

  16. DanJS
    • one year ago
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    3x^2 + 6x - 9 = 0 3*( x^2 + 2x - 3) = 0

  17. Adi3
    • one year ago
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    then what to do next

  18. DanJS
    • one year ago
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    so, x^2 + 2x -3 = 0 you can always just apply the quadratic formula, but this one looks to factor easy

  19. DanJS
    • one year ago
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    (x - 1)*(x+3) = 0

  20. Adi3
    • one year ago
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    wait from where did x-1 come from

  21. DanJS
    • one year ago
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    so, that is true if.. x - 1 = 0 OR x + 3 = 0

  22. DanJS
    • one year ago
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    x = 1 or x=-3

  23. DanJS
    • one year ago
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    factoring a quadratic

  24. Adi3
    • one year ago
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    ohh thanks

  25. DanJS
    • one year ago
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    distribute the thing and check , it goes back to the original

  26. DanJS
    • one year ago
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    or simply just plug in the coefficients to the quadratic equation and hit a button to solve for you

  27. Adi3
    • one year ago
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    i did not get the part after this 3x^2 + 6x - 9 = 0 3*( x^2 + 2x - 3) = 0

  28. Adi3
    • one year ago
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    what did you do after this

  29. DanJS
    • one year ago
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    divide both sides with a 3

  30. DanJS
    • one year ago
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    0/3 = 0

  31. DanJS
    • one year ago
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    Once you get down to standard form ax^2 + bx + c = 0 solving that expression for x will give you the quadratic formula

  32. Adi3
    • one year ago
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    yeah i get it, thanxs

  33. DanJS
    • one year ago
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    \[x = \frac{ -b \pm \sqrt{b^2 - 4*a*c} }{ 2a }\]

  34. DanJS
    • one year ago
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    k, welcome

  35. Adi3
    • one year ago
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    thnxs

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