a Let R R be the subspace of positive reals Show that R is

Solution

a) f(x)=e^x is continuous from R to R+ and has continuous inverse f^-1(x)=ln(x)

b) f(x)=(x-a)/(b-a) is continuous from (a,b) to (0,1) and has continuous inverse f^-1(x)=a+(b-a)x

It also works for part c)