First slide

Functions (XII)

Question

The domain of the function
$f (x) = \sqrt{10 - \sqrt{x^{4} - 21 x^{2}}}$ is

Moderate

A

$[5, \infty)$
B

$[- \sqrt{21}, \sqrt{21}]$
C

$[- 5, \sqrt{21}] \cup [\sqrt{21}, 5] \cup {0}$
D

$(- \infty, - 5)$

Solution

We have,
$x^{4} - 21 x^{2} \geq 0$ and
$10 - \sqrt{x^{4} - 21 x^{2}} \geq 0 \to (1)$
$\Rightarrow x^{2} (x^{2} - 21) \geq 0$ and
$100 \geq x^{4} - 21 x^{2} \to (2)$
$x^{2} (x^{2} - 21) \geq 0$ and
$(x^{2} - 25) (x^{2} + 4) \leq 0$

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