First slide

Functions (XII)

Question

The values of $f (x) = 3 \sin (\sqrt{\frac{π^{2}}{16} - x^{2}})$ lie in the interval

Easy

A

$(0, \frac{3}{\sqrt{2}})$
B

$(\frac{- 3}{\sqrt{2}}, \frac{3}{\sqrt{2}})$
C

$[0, \frac{3}{\sqrt{2}}]$
D

$[\frac{- 3}{\sqrt{2}}, \frac{3}{\sqrt{2}}]$

Solution

$\frac{π^{2}}{16} - x^{2} \geq 0$ $\Rightarrow - \frac{π}{4} \leq \times \leq \frac{π}{4}$
$∴ D_{f} = [- \frac{π}{4}, \frac{π}{4}]$
$f (0) = 3 \sin \frac{π}{4} = \frac{1}{\sqrt{2}} f (\frac{π}{4}) = 3 \sin 0 = 0 r a n g e i s [0, \frac{1}{\sqrt{2}}]$

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