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Math Help - Finding the Inverse of a function when not given what f(x) is

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    Finding the Inverse of a function when not given what f(x) is

    Assume that the function f is a one-to-one function

    If f(6)=4, find f^−1(4).

    and

    The same thing but when given the inverse:

    If f^−1(−2)=−5, find f(−5).
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Lolcats View Post
    Assume that the function f is a one-to-one function

    If f(6)=4, find f^−1(4).

    and

    The same thing but when given the inverse:

    If f^−1(−2)=−5, find f(−5).
    Since the function is injective it has a left-inverse. Thus we have that f(-5)=?\implies -5=f^{-1}(?).
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    Quote Originally Posted by Lolcats View Post
    Assume that the function f is a one-to-one function

    If f(6)=4, find f^−1(4).

    and

    The same thing but when given the inverse:

    If f^−1(−2)=−5, find f(−5).
    Use the definition of "inverse function", of course! That is, if y= f(x) , then x= f^{-1}(y). If 4= f(6), that is, x= 6 and y= 4, f^{-1}(y)= f^{-1}(y)= x= ?.

    Of course, if x= f^{-1}(y) then y= f(x) so the other should be easy now.
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    Thank you! That makes alot of sense!
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