Question

How do you find the domain and range of `x/(x^2+1)`?

Answer 1

The domain is `R` and the range is `[-1/2,1/2]`

Explanation:

The domain is `R` the set of all reals because `1+x^2>0`.

To find the range we have that

`y=x/(x^2+1)=>y(x^2+1)=x=>yx^2+x+y=0=`

this is trinomial with respect to x hence

`1^2-4y*y>=0=>1-4y^2>=0=>-1/2<=y<=1/2`