# question on inverses

• Mar 25th 2009, 06:11 AM
b0mb3rz
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
• Mar 25th 2009, 09:47 AM
stapel
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, 09:56 AM
Inverse functions
Hello b0mb3rz
Quote:

Originally Posted by b0mb3rz
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 $u^{-1}(x) = \frac{x}{c}$