Question

Find the domain of the real valued function: f(x) = $\frac{1}{\sqrt{1 - x^{2}}}$

Answer 1

The $\textbf{domain}$ of function $\textbf{f(x)}$ is the set of all values for which function is defined.

we have to find domain of real valued function : f(x) = $\frac{1}{\sqrt{1-x^2}}$

To define f(x),
denominator of f(x) ≠ 0
and (1 - x²) ≥ 0 [ as we know, square root is possible only of positive terms]

so, (1 - x²) ≠ 0

or, (1 - x)(1 + x) ≠ 0

or, x ≠ -1 , 1

and 1 - x² ≥ 0

or, (1 - x)(1 + x) ≥ 0

or, -1 ≤ x ≤ 1

hence, domain of function $\in [-1,1]-\{-1,1\}$

$\implies$ domain of function $\in$ (-1, 1)