Let `f={(x,x^2/(1+x^2)),x in R}` be a real
function from R to R. Determine the domain
and range of f.

Explanation

`f(x)=y rarr x^2/1+x^2=y rarr x^2=x^2 y+y rarr x^2(1-y)=y rarr x^2=y/1-y`

`x=pm sqrty/1-y`, clearly, `x` will take values if `y/1-y ge 0 rarr 0 le ylt1 rarr y in[0,1) .` Hence, range `(f)=[0,1)`