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Zikro
Lv 5
Zikro asked in Science & MathematicsMathematics · 1 decade ago

Variable based inverses?

Show that, for every value of a, the function

f(x) = a + (1/(x − a))

is its own inverse.

???

1 Answer

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  • Turiski
    Lv 6
    1 decade ago
    Favorite Answer

    g(x) = f^-1(x)

    = a + (1/(x − a))

    f(g(x)) = a + 1/(a + 1/(x − a) − a)

    = a + 1/(a-a + 1/(x-a))

    = a + 1/(1/(x-a))

    = a + (x-a) = x

    And clearly, because g(x) = f(x)

    g(f(x)) = f(g(x))

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