First slide

Functions (XII)

Question

$The range of the function f (x) = \tan \sqrt{\frac{π^{2}}{9} - x^{2}} is$

Easy

A

$[0, \sqrt{3}]$
B

$(0, \sqrt{3})$
C

$[0, \sqrt{3})$
D

$[0, \frac{1}{\sqrt{3}}]$

Solution

$f (x) = \tan \sqrt{\frac{π^{2}}{9} - x^{2}} \Rightarrow \frac{π^{2}}{9} - x^{2} \geq 0 \Rightarrow x^{2} - \frac{π^{2}}{9} \leq 0 \Rightarrow x \in [- \frac{π^{}}{3}, \frac{π^{}}{3}] range of is [0, \sqrt{3}]$

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