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Question
Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\] be a function defined by f(x) = cos [x]. Write range (f).
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Solution
\[\text{Domain} =\left( \frac{- \pi}{2}, \frac{\pi}{2} \right)=\left( - 1 . 57, 1 . 57 \right)(\text{ as } \pi=\frac{22}{7})\]
\[So, \cos \left[ x \right] = \cos \left( - 2 \right) = \cos 2 \forall x \in \left( - 1 . 57, 0 \right)\]
\[\text{Also}, \cos 0 = 1 for x = 0\]
\[\text{And }\cos \left[ x \right] = \cos 1 \forall x \in \left( 0, 1 . 57 \right)\]
\[ \therefore \text{Range}=\left\{ 1, \cos 1, \cos 2 \right\}\]
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