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The domain of $sec^{-1} (2x+1)$, is |
R [-1,1] [-∞, -1]∪ [0, ∞] [-∞, -1]∪ [1, ∞] |
[-∞, -1]∪ [0, ∞] |
The domain of $sec^{-1}x$ is [-∞, -1]∪ [1, ∞]. Therefore, $sec^{-1}(2x+1)$ is meaningful, if $2x + 1 ≥ 1$ or, $2x + 1 ≤ -1$ $⇒ 2x ≥ 0 $ or, $2x ≤ -2$ $⇒x≥0 $ or, $x ≤-1 $ $⇒ x \, ∈ (-∞, -1] ∪ [0, ∞)$ Hence, the domain of $ sec^{-1}(2x+1) $ is $(-∞, -1] ∪ [0, ∞)$. |
