what is the inverse of f(x) = x^2 if the domain is all integers?

Question

hartnn · Answer

range of f(x) cannot be all integers.
so domain of inverse of f(x) can't be all integers

lgbasallote · Answer

....

anonymous · Answer

To find an inverse, you should exchange the y and x values in your equation for f abd solve for y$$y=x ^{2}$$$$x=y ^{2}$$Solve from there.

anonymous · Answer

hartnn, I think the domain refers to f of x 's domain...?

hartnn · Answer

if you allow complex values, then its $\sqrt x$

lgbasallote · Answer

enlighten me

hartnn · Answer

like square of complex numbers can be negative.
then x^2 can take negative integers and $\sqrt x $ will have the domain of negative integers also

lgbasallote · Answer

you lost me...

ganeshie8 · Answer

there is no inverse

lgbasallote · Answer

why so

anonymous · Answer

there is no inverse...

ganeshie8 · Answer

y = x^2 doesnt pass horizontal line test, in the domain of integers

hartnn · Answer

i^2 = -1
so 
if we allow x=i
x^2 is negative
then range of f(x) can be negative integers, so domain of f^-1(x) can be all integers....

anonymous · Answer

@ganeshie8 , Neither do inverse trig functions, but we can still find an inverse on an interval..

anonymous · Answer

the domain of f(x) will be the range of f^-1(x) if it exists....f^-1(x) can be sqrt(x) but its range should be positive integers but not all integers....complex plays no role here..

lgbasallote · Answer

makes sense