1. inverse

is it true Always?

$ff^{-1}(x)=x ~~~ and~~~ f^{-1}f(x)=x$

I dont know. because i see

$f(x)=x^2 ~~~ f^{-1}(x)=\sqrt{x},~~\\ f^{-1}f(x)=x,-x\neq x$

when is it $ff^{-1}(x)=x ~~~ and~~~ f^{-1}f(x)=x$ ??

thanks

2. Re: inverse

f(x)=x^2 isn't one to one for all x and so doesn't have an inverse for all x. You need to restrict x to a given domain over which it is one to one
For example f(x)=x^2, x>0.

3. Re: inverse

Originally Posted by biffboy
f(x)=x^2 isn't one to one for all x and so doesn't have an inverse for all x. You need to restrict x to a given domain over which it is one to one
For example f(x)=x^2, x>0.
thanks . if f is one to one then is it true always?

Yes it is.