First slide

Properties of ITF

Question

The value of x for which $\cos^{- 1} (\cos 4) > 3 x^{2} - 4 x is$

Moderate

A

$(0, \frac{2 + \sqrt{6 π - 8}}{3})$
B

$(\frac{2 - \sqrt{6 π - 8}}{3}, 0)$
C

(-2, 2)
D

$(\frac{2 - \sqrt{6 π - 8}}{3}, \frac{2 + \sqrt{6 π - 8}}{3})$

Solution

$Now, \cos^{- 1} (\cos 4) = \cos^{- 1} {\cos (2 π - 4)} = 2 π - 4 \begin{array}{ll} \Rightarrow & 2 π - 4 > 3 x^{2} - 4 x \\ \Rightarrow & 3 x^{2} - 4 x - (2 π - 4) < 0 \\ \Rightarrow & \frac{2 - \sqrt{6 π - 8}}{3} < x < \frac{2 + \sqrt{6 π - 8}}{3} \end{array}$

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