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Math Help - Need help about functions..!

  1. #1
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    Need help about functions..!

    Hi all, can someone please give description about the use of composite and inverse functions with examples...? any help will be appreciated
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    Re: Need help about functions..!

    I like to think of composit functions as one function inside another.

    Consider f(x)= x^2 and g(x) = \cos x then f(g(x))  =  g(x)^2  = (\cos x)^2 is a composite function



    For an inverse function, think about what the inverse of an operation is. If I square something the inverse operation is a square root. Therefore when thinking about functions i.e. f(x) =x^2 then the inverse is f^{-1}(x) = \sqrt{x}
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  3. #3
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    Re: Need help about functions..!

    "Square" and "square root" are not good examples here. For example, if x= -2, then x^2= 4 and then \sqrt{4}= 2, not -2. That's because [itex]f(x)= x^2[/itex] is not "one-to-one"- both 2^2 and (-2)^2 give four- so it does not have a true "inverse". A better example would be "cube" and "cube root". For any real number x, \sqrt[3]{x^3}= \left(\sqrt[3]{2}\right)^3.
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    Re: Need help about functions..!

    Thanks HOI, a good point you raise.

    Inverse functions only exist when a function is one to one. My example was not entirely correct, although should give you a taste of what it's all about.
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