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Jamierox4ev3r

  • one year ago

Find the composition of f(g(x)), when f(x)=7x^2-2x+9 and g(x)=x-4 Simplify

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  1. Jamierox4ev3r
    • one year ago
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    I have a pretty clear idea of how to go about doing this, so I'll just show all of my process. I'll also point out the one small detail that I had a bit of doubt on.

  2. Jamierox4ev3r
    • one year ago
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    \(7(x-4)^{2}-2(x-4)+9\) \(7(x-4)(x-4)-2x+8+9\) \((7x-28)(x-4)-2x+17\) \(7x^{2}-28x-28x+112-2x+17\) \(7x^{2}-58x+129\) ^^ I believe this is correct...but I forget the rules on difference of squares. does (x-2)^2 turn into (x-2)(x-2) or (x-2)(x+2) ?? Also, do I need to factor the final answer?

  3. madhu.mukherjee.946
    • one year ago
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    try and see if it can be done,then its good

  4. Jamierox4ev3r
    • one year ago
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    see it what can be done?

  5. madhu.mukherjee.946
    • one year ago
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    i don't think it can be factored

  6. jim_thompson5910
    • one year ago
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    x^2 means x times x anything squared is that number multiplied by itself so (x-2)^2 means (x-2) times (x-2)

  7. jim_thompson5910
    • one year ago
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    \[\Large 7x^{2}-58x+129\] is the correct final answer

  8. Jamierox4ev3r
    • one year ago
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    Oh. You're referring to my question on whether it could be factor or not. oh and @jim_thompson5910 , so in the problem, if you look at my work, my assumption was indeed that (x-2)^2 was (x-2)(x-2). Thank you! I thought I remembered some funky rule from early high school about difference of squares or something like that. So I was correct all along. Wow I overthought this. Thank again!

  9. jim_thompson5910
    • one year ago
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    you're thinking of a^2 - b^2 = (a-b)(a+b)

  10. madhu.mukherjee.946
    • one year ago
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    its perfectly all right

  11. madhu.mukherjee.946
    • one year ago
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    u can solve it by the formula

  12. Jamierox4ev3r
    • one year ago
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    Oh okay. These rules are so easy to get confused, especially when trying to recall from memory

  13. madhu.mukherjee.946
    • one year ago
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    this formula is known as the SRIDHAR ACHARYA formula

  14. madhu.mukherjee.946
    • one year ago
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    don't worry by this formula it will get easy

  15. madhu.mukherjee.946
    • one year ago
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    put 7x^-58x+129 in this formula

  16. Jamierox4ev3r
    • one year ago
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    Don't you mean the quadratic formula? And yes, I know that you can use the quadratic formula to factor. Problem is, I see now that when I use the quadratic formula, the roots are imaginary. Therefore, This cannot be factored any further. Jim's answer is the final answer

  17. madhu.mukherjee.946
    • one year ago
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    yeah

  18. Jamierox4ev3r
    • one year ago
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    @madhu.mukherjee.946 thanks for trying to help, but I fully understand now. I've used the quadratic formula before, and I understand what it does \(\ddot\smile\)

  19. madhu.mukherjee.946
    • one year ago
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    okay.your welcome

  20. jim_thompson5910
    • one year ago
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    You can use the discriminant formula as a shorter way to see if you can factor or not if D = b^2 - 4ac is a perfect square and a positive number, then you can factor

  21. Jamierox4ev3r
    • one year ago
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    Woah, that's a helpful tip. *cough* I have a program in my calculator that solves all quadratics for me, so that's how I knew that the roots would be imaginary. But when in a pinch, when without a calculator, this is an extremely convenient tip. Thanks for bringing that back into my memory

  22. jim_thompson5910
    • one year ago
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    definitely a handy thing to have

  23. jim_thompson5910
    • one year ago
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    you're welcome

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