The correct option is (a)
![\[\left[ \mathbf{1},\text{ }\mathbf{2} \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fcfcb28dd59583bc3e7a020a8cf5f451_l3.png "Rendered by QuickLaTeX.com")
We know that,
![\[si{{n}^{-1}}~x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-958bbea3ced100668e06cb5f9488bb6d_l3.png "Rendered by QuickLaTeX.com")
is defined for
![\[x\in \left[ -1,\text{ }1 \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-de1bcbd2b1e5c0dbe24fa638267ab771_l3.png "Rendered by QuickLaTeX.com")
So, f(x) =
![\[\mathbf{si}{{\mathbf{n}}^{-\mathbf{1}}}~\sqrt{\left( \mathbf{x}\text{ }\text{ }\mathbf{1} \right)}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dfbf35cc7cb2d872feaf569485ef4904_l3.png "Rendered by QuickLaTeX.com")
is defined if
![\[<span class="ql-right-eqno"> (1) </span><span class="ql-left-eqno"> </span><img src="https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8a0869979131ceddb0dd11dc8f006c30_l3.png" height="124" width="281" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} & \begin{array}{*{35}{l}} 0\text{ }\le \text{ }\sqrt{\left( x\text{ }\text{ }1 \right)}\text{ }\le \text{ }1 \\ 0\text{ }\le \text{ }x\text{ }\text{ }1\text{ }\le \text{ }1 \\ \end{array} \\ & 1\text{ }\le \text{ }x\text{ }\le \text{ }2 \\ \end{align*}" title="Rendered by QuickLaTeX.com"/>\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-946ee8c5c275727d2b880902c10821ed_l3.png "Rendered by QuickLaTeX.com")
Hence,
![\[x\in \left[ 1,\text{ }2 \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-859851df4d7338f63b1a97ea187bf561_l3.png "Rendered by QuickLaTeX.com")
The domain of the function by f(x) =
![\[\left[ -\mathbf{1},\text{ }\mathbf{1} \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b21f7411312e08e9e9c76b1a5369f211_l3.png "Rendered by QuickLaTeX.com")
![\[\left[ \mathbf{0},\text{ }\mathbf{1} \right]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4951cedbbb831e919142a21d14151c6a_l3.png "Rendered by QuickLaTeX.com")
The correct option is (a)
We know that,
is defined for
So, f(x) =
is defined if
Hence,
