First slide

Functions (XII)

Question

The domain of f(x)= $\sqrt{x - x^{2}}$ + $\sqrt{4 + x}$ + $\sqrt{4 - x}$

Moderate

A

[-4, $\infty)$
B

(-4,4]
C

[0,4]
D

[0,1]

Solution

Given, f(x)= $\sqrt{x - x^{2}}$ + $\sqrt{4 + x}$ $\sqrt{4 - x}$ $\Rightarrow x - x^{2} \geq 0$ and 4+x $\geq$ 0 and 4-x $\geq$ 0
$\Rightarrow x (1 - x) \geq 0 a n d x \geq - 4 a n d x \leq 4$
$\Rightarrow x (x - 1) \leq 0, x \geq - 4, x \leq 4$
$\Rightarrow x \in [0, 1], x \geq - 4, x \leq 4$

$∴$ x $\in$ $[0, 1]$

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