What is the domain and range of $f (x) = \frac{1}{1 + x^{2}}$ $f(x) = 1/(1+x^2)$ ?

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Answer 1 · 2016-02-14T12:57:49

Domain: $- \infty < x < + \infty$ $-oo < x < +oo$

Range: $1 \geq f (x) > 0$ $1 >=f(x) >0$

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

$x^{2}$ $x^2$ can only be such that $0 \leq - x^{2} < \infty$ $0<=-x^2< oo$ .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

What is the domain and range of f(x) = 1/(1+x^2)f(x)=11+x2f(x) = 1/(1+x^2)?