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Math Help - Prove that function is inverse of itself?

  1. #1
    Super Member fardeen_gen's Avatar
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    Prove that function is inverse of itself?

    Show that the function given by f(x) = \frac{k}{x},\ f:\mathbb{R} - \{0\}\rightarrow \mathbb{R} - \{0\}, where k\in\mathbb{R}, k\neq 0 is inverse of itself.
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    Quote Originally Posted by fardeen_gen View Post
    Show that the function given by f(x) = \frac{k}{x},\ f:\mathbb{R} - \{0\}\rightarrow \mathbb{R} - \{0\}, where k\in\mathbb{R}, k\neq 0 is inverse of itself.
    How have you been taught to find the inverse of a function and where are you stuck in that procedure?
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    Senior Member Sampras's Avatar
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     f(f(x)) = x e.g. it is the identity element. This is given that we know  f is its own inverse.
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    Quote Originally Posted by fardeen_gen View Post
    Show that the function given by f(x) = \frac{k}{x},\ f:\mathbb{R} - \{0\}\rightarrow \mathbb{R} - \{0\}, where k\in\mathbb{R}, k\neq 0 is inverse of itself.
    For two functions, g(x) and f(x), to be inverses of eachother, g(f(x))=x and f(g(x))=x

    So if f(x) is it's own inverse, then f(f(x))=x and swapping the order, f(f(x))=x, which is the same identity.

    So f(f(x))= f\left(\frac{k}{x}\right)=\frac{k}{\frac{k}{x}}=\f  rac{k}{\frac{k}{x}}*\frac{x}{x}=\frac{kx}{k}=x
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    Quote Originally Posted by Sampras View Post
     f(f(x)) = x e.g. it is the identity element. This is given that we know  f is its own inverse.
    No
    We want(ed) to prove it...
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