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  • Perplex

    Function Theory (Lesson 4/4)

    Inverse Functions

    1 / 9

    Discussion

    If ​f−1, the inverse of ​f, is the function that "undoes" ​f​ and it is given that ​f(a)=b, find ​f−1(b).

    Solution:

    The inverse function undoes whatever ​f​ does: if ​y=f(x), then ​f−1(y)=x. Substituting ​a​ and ​b​ for ​x​ and ​y​ yields: if ​b=f(a), then ​​​f−1(b)=a.


    Since we are given that ​f(a)=b, we must have

    ​
    f−1(b)=a.
    ​