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Math Help - Find the Inverse Function

  1. #1
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    Find the Inverse Function

    Find the inverse of the function f(x) = sqrt{r^2 - x^2}, where 0 < or = to x < or = to r
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello !
    Quote Originally Posted by magentarita View Post
    Find the inverse of the function f(x) = sqrt{r^2 - x^2}, where 0 < or = to x < or = to r
    Why are you stuck ? As f is a bijection on [0,r] (Can you show this ?) its inverse function exists. Let y=f(x) : we're asked to find the inverse function of f that is the function g such that x=g(y). This can simply be done by solving y=\sqrt{r^2-x^2} for x :

    \begin{aligned}<br />
y=\sqrt{r^2-x^2} & \Longleftrightarrow y^2=r^2-x^2\\<br />
&\Longleftrightarrow x^2=\ldots\\<br />
&\Longleftrightarrow x=\ldots<br />
\end{aligned}

    hence the inverse function of f is ...
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  3. #3
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    Bijection???

    What is bijection? Our teacher never used that word in class.
    Please explain.
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  4. #4
    Senior Member nikhil's Avatar
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    Bijection means being both one to one and onto.
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  5. #5
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    nikhil

    nikhil:

    You said:

    "Bijection means being both one to one and onto."

    This statement is not too clear.

    Can you break it down a little more for those of us who are not math majors?
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  6. #6
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    Quote Originally Posted by magentarita View Post
    nikhil:

    You said:

    "Bijection means being both one to one and onto."

    This statement is not too clear.

    Can you break it down a little more for those of us who are not math majors?
    One-to-one and Onto Functions
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  7. #7
    Senior Member nikhil's Avatar
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    Quote Originally Posted by magentarita View Post
    nikhil:

    You said:

    "Bijection means being both one to one and onto."

    This statement is not too clear.

    Can you break it down a little more for those of us who are not math majors?
    1) one to one
    it means each element of domain will have a unique image in codomain.no two elements of domain can have the same image in codomain.
    2) onto
    it means each element of codomain will surely have a preimage in the domain.no element of codomain will left unlinked with element of domain.
    I hope this helps.if still there is any problem then you may ask it freely.
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  8. #8
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    Finally...

    I finally get it.

    Thanks
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