Math, asked by PragyaTbia, 1 year ago

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

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Answered by abhi178
0
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)
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