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Math Help - question on inverses

  1. #1
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    question on inverses

    suppose f: R-->R is invertible and C Є R is a constant
    find an expression for the inverse of g(x) = f(x+c) in terms of f^-1
    and if c is not equal to 0 than find an expression for the inverse of h(x) =f(cx) in terms of f^-1

    thanks
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  2. #2
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    Hint: f(x + c) = f(h(x)) for h = x + c, and f^{-1} = (f(h))^{-1} = h^{-1}(f^{-1}).

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  3. #3
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    Inverse functions

    Hello b0mb3rz
    Quote Originally Posted by b0mb3rz View Post
    suppose f: R-->R is invertible and C Є R is a constant
    find an expression for the inverse of g(x) = f(x+c) in terms of f^-1
    and if c is not equal to 0 than find an expression for the inverse of h(x) =f(cx) in terms of f^-1

    thanks
    Suppose that t(x) = x + c. Then t^{-1}(x) = x-c

    g(x) = f(x+c) = f\Big(t(x)\Big) = ft(x)

    \Rightarrow g^{-1}(x) = (ft)^{-1}(x)

    = t^{-1}f^{-1}(x)

    = t^{-1}\Big(f^{-1}(x)\Big)

    = f^{-1}(x) - c

    Do the second part in a similar way, starting with u(x) = cx, and so u^{-1}(x) = \frac{x}{c}

    Grandad
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