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Math Help - Polynomial

  1. #1
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    Polynomial

    Real quick question

    Given that f(x) = 5x^2 - 12

    i) what is the degree of this polnomial ? ( Is this 2?)

    iii) with the aid of a flow chart, or otherwise , write down the expression for f^-1(x).

    What does the f^-1 mean?

    cheers for all the help guys.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by mxmadman_44 View Post
    Real quick question

    Given that f(x) = 5x^2 - 12

    i) what is the degree of this polnomial ? ( Is this 2?)
    The degree of a polynomial is the largest sum of the exponents of the terms. In this case, there is only one variable, so its simple: the largest exponent is 2, so this is a polynomial of degree 2, or a quadratic.

    Quote Originally Posted by mxmadman_44 View Post
    iii) with the aid of a flow chart, or otherwise , write down the expression for f^-1(x).

    What does the f^-1 mean?

    cheers for all the help guys.
    What happened to question ii)?
    The notation f^{-1}(x) indicates the inverse function. The inverse function has the property that, if y = f(x) then f^{-1}(y) = x.

    There's an algebraic method of finding these.

    Let
    y = f(x) = 5x^2 - 12

    Now exchange the roles of x and y:
    x = 5y^2 - 12

    Now solve for y:
    5y^2 = x + 12

    y^2 = \frac{x + 12}{5}

    y = \sqrt{\frac{x + 12}{5}}

    Now we have that f^{-1}(x) = y = \sqrt{\frac{x + 12}{5}}.

    (Note: We really need to be a bit more careful than I was about domains and ranges. If you need more accuracy here, just let me know.)

    -Dan
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  3. #3
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    i is good. The degree is 2

    f^{-1}(x) indicates the Inverse Function, the lovely function that gives you back whatever f(x) did to the value in the fisrt place.

    For example:

    f(x) = 2x

    f^{-1}(x) = x/2

    f(6) = 12 and f^{-1}(12) = 6

    See how we got back what we started with?

    The usual methodology is "Swap and Solve"

    If y = 5x^{2} - 12, then REsolve for 'y' in x = 5y^{2} - 12. This will give you an Inverse RELATION. The result that it is or is not a function is an additional important consideration that will cause you problems on this one. Solve that last expression for "y" and see if you can tell why it's a problem.
    Last edited by TKHunny; August 16th 2007 at 09:47 AM. Reason: Typo
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  4. #4
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    thanks

    thanks guys i understand it now. It all came rushing back to me. My notes were not so clear but i completely understand it now

    thankyou
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