find domain and range of function f= {(x, 1/1-x2):x belongs to R - Maths - Relations and Functions

Question

find domain and range of function f= {(x, 1/1-x
2 ):x belongs to R?

Gursheen kaur. · Accepted Answer

$f (x) = \frac{1}{1 - x^{2}} H e r e, 1 - x^{2} = 0 1 = x^{2} x = \pm 1 D_{f} = R - {- 1, 1}$

Now, Let y = f(x)

then

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

Hence, range of f(x) is all real nos. : y <0 and y≥1

find domain and range of function f= {(x, 1/1-x 2 ):x belongs to R?