Results 1 to 4 of 4

Thread: Polynomial

  1. #1
    Newbie
    Joined
    Feb 2007
    Posts
    22

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    11,152
    Thanks
    731
    Awards
    1
    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 $\displaystyle f^{-1}(x)$ indicates the inverse function. The inverse function has the property that, if $\displaystyle y = f(x)$ then $\displaystyle f^{-1}(y) = x$.

    There's an algebraic method of finding these.

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

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

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

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

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

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

    (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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    i is good. The degree is 2

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

    For example:

    $\displaystyle f(x) = 2x$

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

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

    See how we got back what we started with?

    The usual methodology is "Swap and Solve"

    If $\displaystyle y = 5x^{2} - 12$, then REsolve for 'y' in $\displaystyle x = 5y^{2} - 12$. 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; Aug 16th 2007 at 08:47 AM. Reason: Typo
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2007
    Posts
    22

    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Oct 23rd 2011, 06:36 AM
  2. Replies: 1
    Last Post: Feb 24th 2011, 06:46 PM
  3. Replies: 1
    Last Post: Dec 15th 2009, 07:26 AM
  4. [SOLVED] dividing polynomial by a polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Feb 3rd 2008, 02:00 PM
  5. dividing a polynomial by a polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Aug 2nd 2005, 12:26 AM

Search Tags


/mathhelpforum @mathhelpforum