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26 July, 19:40

Find the inverse of f (x) = - x + 3

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  1. 26 July, 23:18
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    Let g the inverse function of f.

    The most important property of g and f being inverses of each other, is that

    g (f (x)) = x, also f (g (x)) = x

    so, what one function 'does' to x, the other 'undoes' it.

    Thus, we have:

    f (g (x)) = x and alos f (g (x)) = - g (x) + 3, from the rule

    thus:

    -g (x) + 3=x

    -g (x) = x-3

    g (x) = - x+3

    check: f (g (x)) = f (-x+3) = - (-x+3) + 3=x-3+3=x

    Answer: the inverse of f is g, such that g (x) = - x+3
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