The domain of the function$f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - 1}}\left( {{{x - 1} \over {x + 1}}} \right)$ is :

Question

The domain of the function

$f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - 1}}\left( {{{x - 1} \over {x + 1}}} \right)$ is :

$\left[ {0,{1 \over 4}} \right]$

$[ - 2,0] \cup \left[ {{1 \over 4},{1 \over 2}} \right]$

$\left[ {{1 \over 4},{1 \over 2}} \right] \cup \{ 0\} $

$\left[ {0,{1 \over 2}} \right]$

Solution

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