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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- Mar 25th 2009, 05:11 AMb0mb3rzquestion 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 - Mar 25th 2009, 08:47 AMstapel
Hint: f(x + c) = f(h(x)) for h = x + c, and f^{-1} = (f(h))^{-1} = h^{-1}(f^{-1}).

(Wink) - Mar 25th 2009, 08:56 AMGrandadInverse functions
Hello b0mb3rzSuppose that $\displaystyle t(x) = x + c$. Then $\displaystyle t^{-1}(x) = x-c$

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

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

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

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

$\displaystyle = f^{-1}(x) - c$

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

Grandad