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domain of sqrt (4/1-x)+3/(1+x)+(x/1-x^2) is... what will be the answer

domain of sqrt (4/1-x)+3/(1+x)+(x/1-x^2) is... what will be the answer

Grade:12th pass

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
6 years ago
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Samyak Jain
333 Points
6 years ago
Let f(x) = \sqrt{}{4 / (1-x)} + {3 / (1 + x)}+{x / (1-x2)}
For the domain of f(x), the term inside the sqr root should be positive.
\therefore {4 / (1-x)} + {3 / (1 + x)} + {x / (1-x2)} > 0
{4 / (1-x)}*(1 + x) + {3 / (1 + x)}*(1 – x) + {x / (1-x2)} > 0
(4 + 4x + 3 – 3x + x) / (1 – x2) > 0 
(2x + 7) / (1- x2) > 0  or  (2x + 7) / (x2 - 1 )
i.e. (2x + 7) (x2 - 1 ) > 0 ;      (2x + 7) (x + 1) (x – 1) > 0
\therefore x \epsilon (- infinity, -7/2)  \cup  (-1,1)

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