First slide

Functions (XII)

Question

Part of the domain of the function $f (x) = \sqrt{\frac{\cos x - 1 / 2}{6 + 35 x - 6 x^{2}}}$ lying in the interval [–1, 6] is

Moderate

A

$[- 1 / 6, π / 3] \cup [5 π / 3, 6]$
B

$(- 1 / 6, p / 3] » [5 p / 3, 6)$
C

(–1/6, 6)
D

none of these

Solution

The function f is meaningful only if $\cos x - 1 / 2 \geq 0, 6 + 35 x 6 x^{2} > 0$
or $\cos x - 1 / 2 \leq 0, 6 + 35 x 6 x^{2} < 0$
i. e. , $\cos x \geq 1 / 2, (6 - x) (1 + 6 x) > 0$ or $\cos x \leq 1 / 2, (6 - x)$ $(1 + 6 x) < 0$
These inequalities are satisfied if $x \in (- 1 / 6, π / 3] \cup [5 π / 3, 6)$

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