Question

Find domain and range of function 1/(1-x^2)​

Answer 1

Step-by-step explanation:

Given function

$f(x) = \dfrac{1}{1 - {x}^{2} }$

Clearly, f(x) is not defined when

$1 - {x}^{2} = 0$

i.e., x = ± 1

.°. dom ( f ) = R - { -1, 1 }

Also,

$y = \dfrac{1}{1 - {x}^{2} } \\ \\ = > 1 - {x}^{2} = \dfrac{1}{y} \\ \\ = > x = \sqrt{1 - \frac{ 1}{y} }$

Clearly, x is not defined when

$1 - \dfrac{1}{y} < 0 \: \: \: or \: \: \: 1 < \dfrac{1}{y} \: \: \: or \: \: \: y < 1$

.°. range( f )= R - {y € R : y < 1} = {y € R : y ≥ 1}