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The domain of the function \[\mathbf{cos}-\mathbf{1}\text{ }\left( \mathbf{2x}-\text{ }\text{ }\mathbf{1} \right)\]is (a) \[\left[ \mathbf{0},\text{ }\mathbf{1} \right]\] (b) \[\left[ -\mathbf{1},\text{ }\mathbf{1} \right]\] (c) \[\left[ -\mathbf{1},\text{ }\mathbf{1} \right]\] (d) \[\left[ \mathbf{0},\text{ }\mathbf{\pi } \right]\]
The domain of the function \[\mathbf{cos}-\mathbf{1}\text{ }\left( \mathbf{2x}-\text{ }\text{ }\mathbf{1} \right)\]is (a) \[\left[ \mathbf{0},\text{ }\mathbf{1} \right]\] (b) \[\left[ -\mathbf{1},\text{ }\mathbf{1} \right]\] (c) \[\left[ -\mathbf{1},\text{ }\mathbf{1} \right]\] (d) \[\left[ \mathbf{0},\text{ }\mathbf{\pi } \right]\]
CBSE | Class 12 | Exercise 1 | Inverse Trigonometric Functions | Maths | NCERT Exemplar
The domain of the function \[\mathbf{cos}-\mathbf{1}\text{ }\left( \mathbf{2x}-\text{ }\text{ }\mathbf{1} \right)\]is (a) \[\left[ \mathbf{0},\text{ }\mathbf{1} \right]\] (b) \[\left[ -\mathbf{1},\text{ }\mathbf{1} \right]\] (c) \[\left[ -\mathbf{1},\text{ }\mathbf{1} \right]\] (d) \[\left[ \mathbf{0},\text{ }\mathbf{\pi } \right]\]

The correct option is  (a) \[\left[ \mathbf{0},\text{ }\mathbf{1} \right]\]

Since, \[cos-1\text{ }x\] is defined for \[x\in \left[ -1,\text{ }1 \right]\]

So, f(x) = \[\mathbf{cos}-\mathbf{1}\text{ }\left( \mathbf{2x-}\text{ }\text{ }\mathbf{1} \right)\]is defined if

\[\begin{array}{*{35}{l}}

-1\text{ }\le \text{ }2x\text{ }\text{ }-1\text{ }\le \text{ }1  \\

0\text{ }\le \text{ }2x\text{ }\le \text{ }2  \\

\end{array}\]

Hence,

\[0\text{ }\le \text{ }x\text{ }\le \text{ }1\]

i

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