Question

What is the domain and range of `f(x) = 1/(1+x^2)`?

Answer 1

Domain: `-oo < x < +oo`

Range: `1 >=f(x) >0`

Explanation:

The basic 'rule' is that you are not 'allowed' to divide by 0. The proper term for this is that it is not defined.

`x^2` can only be such that `0<=-x^2< oo` .This is true for any value of `{x: x in RR)`

When `x`=0 then `f(x)=1`.
As `x^2` increases then `1/(1+x^2)` reduces and eventually will tend to 0