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Domain of $\cos^{−1}[2x^2 − 3]$ where [.] denotes greatest integer function, is |
$\left[1,\sqrt{\frac{5}{2}}\right]$ $\left[-\sqrt{\frac{5}{2}},-1\right]$ $\left(-\sqrt{\frac{5}{2}},-1\right]∪\left[1,\sqrt{\frac{5}{2}}\right)$ none of these |
$\left(-\sqrt{\frac{5}{2}},-1\right]∪\left[1,\sqrt{\frac{5}{2}}\right)$ |
We have, $−1 ≤ [2x^2 − 3] ≤ 1 ⇒ −1 ≤ 2x^2 − 3 < 2 ⇒ 1 ≤ x^2<\frac{5}{2}$ $⇒x∈\left(-\sqrt{\frac{5}{2}},-1\right]∪\left[1,\sqrt{\frac{5}{2}}\right)$ |
