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    why is that when i want to solve for value of x so a function equals its inverse function

    f(x) = f-1(x) (the -1 is suppose to be small)

    how come the inverse function can be substituted with x?

    for example , f(x) = x^2 - 3

    √x+3 = x^2 - 3 can be worked out with x^2 - 3 = x

    why is f(x) = f-1(x) equals to f(x) = x ?


    could that be because the x and y are reversed in inverse function so by inputting x value i'm actually imputing its y value and outputting the x value?
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    (Original post by alvan15)
    why is that when i want to solve for value of x so a function equals its inverse function
    Look at the graph of f(x) and f^{-1}(x). You'll see that they intersect only along the line y=x. Hence any solution to f(x) = f^{-1}(x) will be equivalent to f(x) = x or f^{-1}(x) = x.

    This phenomenon occurs precisely due to the definition of what it means for a function to be an inverse to another. Specifically, their composition is the identity.
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    [QUOTE=Zacken;69983322]
    (Original post by alvan15)
    why is that when i want to solve for value of x so a function equals its inverse function
    /QUOTE]

    Look at the graph of f(x) and f^{-1}(x). You'll see that they intersect only along the line y=x. Hence any solution to f(x) = f^{-1}(x) will be equivalent to f(x) = x or f^{-1}(x) = x.

    This phenomenon occurs precisely due to the definition of what it means for a function to be an inverse to another. Specifically, their composition is the identity.
    thank you so much , i totally get it now , appreciate the help, have a nice day
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    (Original post by alvan15)
    thank you so much , i totally get it now , appreciate the help, have a nice day
    No problem
 
 
 
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