Question

Find the domain of the function:

f(x)= 1/(√x²-1)

Answer 1

For this function to be defined,

1.

Denominator should not be equal to 0.

√(x^2–1) should not be equal to 0.

√x^2-1 != 0 (!= Mens not equal to)

x^2–1 != 0.

(x+1)(x-1) !=0

X != 1 and -1.

2.

For root function to be defined…

Root do not contains negative values.

x^2–1>=0

(x+1)(x-1)>=0

Therefore x lies between (-infinity,-1) U (1,infinity).

From 1 and 2 ,we get domain of the function as

( -infinity,-1) U (1,infinity).