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anonymous

  • one year ago

If f(x) = x2 – 1 and g(x) = 2x – 3, what is the domain of (f*g)(x)

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  1. SolomonZelman
    • one year ago
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    you are multiplying a polynomial times another polynomial. This will give you a polynomial as well.

  2. anonymous
    • one year ago
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    ok

  3. SolomonZelman
    • one year ago
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    You know what polynomial is, correct?

  4. anonymous
    • one year ago
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    yes

  5. SolomonZelman
    • one year ago
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    Ok, will you agree with me (if you don't understand why it is so, then ask! but will you agree) that a polynomial is DEFINED for ALL values of x?

  6. anonymous
    • one year ago
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    why is it so? haha

  7. SolomonZelman
    • one year ago
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    Ok, i will post a percise and short definition of a polynomial. "Polynomial" is a function that can have the terms of: 1) Constants (some real numbers) 2) x raised to a power of 1, 2, 3 and on (but the power has to be a whole number) (and the terms can have any real coefficients)

  8. SolomonZelman
    • one year ago
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    i will do some examples

  9. anonymous
    • one year ago
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    ok

  10. SolomonZelman
    • one year ago
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    polynomials. examples. y=0 y=-45 y=√3 (or any function y=c where c is a constant) y=-4x y=3x+2 y=x-9 (or any function in a form of y=mx or y=mx+b) y=3x² y=-5x²+9 y=x²+8 y=x²-7x-7 and so on....

  11. anonymous
    • one year ago
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    ok im pretty sure i get it

  12. SolomonZelman
    • one year ago
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    it (a polynomial) terms can be made up and can consist of any terms as long as the terms have x^(whole number) and other real numbers ok got the definition

  13. anonymous
    • one year ago
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    ok

  14. SolomonZelman
    • one year ago
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    So, really try to think of any polynomial that can have an UNDEFINED X-VALUE. what I mean by "UNDEFINED X-VALUE" is that if you plug this value for x into the function, then you will get an undefined/indeterminate output for y in polynomials this "UNDEFINED X-VALUE" never exists

  15. anonymous
    • one year ago
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    okay

  16. SolomonZelman
    • one year ago
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    Because if your x's have only whole number powers such as: x\(^1\), x\(^2\), x\(^3\), x\(^4\) then you will get a valid result NO MATTER WHAT you plug in for x.

  17. anonymous
    • one year ago
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    okay makes sense

  18. SolomonZelman
    • one year ago
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    now agin, when you multiply two functions where both of these functions are polynomials (i.e. whole number powers of x like 1, 2, 3 and on with or without constants) then you get after multiplying these two (or any number of) polynomial functions - you will get - a polynomial function (whole number powers of x like 1, 2, 3 and on with or without constants)

  19. anonymous
    • one year ago
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    ok

  20. SolomonZelman
    • one year ago
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    polynomial • polynomial = polynomial it is good to remember, even if you don't fully comprehend the deepness behind it (you will get it at some time)

  21. SolomonZelman
    • one year ago
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    now, if your function f(x)=x²-1 and g(x)=2x-3 polynomial?

  22. SolomonZelman
    • one year ago
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    are the polynomials?

  23. anonymous
    • one year ago
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    yes

  24. anonymous
    • one year ago
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    they are

  25. SolomonZelman
    • one year ago
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    so the product of them (when you multiply f • g) will also give you a what?

  26. anonymous
    • one year ago
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    polynomial

  27. SolomonZelman
    • one year ago
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    yes.

  28. SolomonZelman
    • one year ago
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    And again, ANY POLYNOMIAL has a domain of ALL VALUES OF X. (in interval notation: Domain: (-∞, +∞) )

  29. SolomonZelman
    • one year ago
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    So will what be the domain of your new function be? (we know your new function is going to be a polynomial -as we said b4)

  30. SolomonZelman
    • one year ago
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    if you got questions, you can always ask ....

  31. anonymous
    • one year ago
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    im following as of right now :)

  32. SolomonZelman
    • one year ago
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    we know your function is a polynomial (correct?) So can you give me the domain of your new function, or not yet?

  33. anonymous
    • one year ago
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    (-∞, +∞)?

  34. SolomonZelman
    • one year ago
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    yes

  35. SolomonZelman
    • one year ago
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    the ∞ (or +∞) symbol means infinity and -∞ means negative infinity --> (same stength but going the negative way)

  36. anonymous
    • one year ago
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    okay i remember that one

  37. SolomonZelman
    • one year ago
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    (-∞, +∞) means from negative infinity to positive infinity and that is: every single number that there can possible be

  38. anonymous
    • one year ago
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    i wish you were my math teacher haha

  39. SolomonZelman
    • one year ago
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    that is the domain of your new polynomail function, or of any polynomial function.....

  40. SolomonZelman
    • one year ago
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    i am just some 19 yrs old dude....

  41. anonymous
    • one year ago
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    YOUR ONLY 19!!!!

  42. SolomonZelman
    • one year ago
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    Math is just something I like:) In any case, do you have questions regarding this question?

  43. anonymous
    • one year ago
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    nope i got it :) ty so much

  44. SolomonZelman
    • one year ago
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    k, yw

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