Question

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

is

• A. $\lbrack - 4,\infty)$
• B. $\lbrack - 4,4\rbrack$
• C. $\lbrack 0,4\rbrack$
• D. $\lbrack 0,1\rbrack$

Answer 1

Answer: (D)

$\lbrack 0,1\rbrack$

Answer 2

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

clearly $f(x)$ is defined if

$4 + x \geq 0$ ⇒ $x \geq - 4$

$4 - x \geq 0$ ⇒ $x \leq 4$

$x(1 - x) \geq 0$ ⇒ $x \geq 0$ and $x \leq 1$

∴ Domain of $f = ( - \infty,4\rbrack \cap \lbrack - 4,\infty) \cap \lbrack 0,1\rbrack = \lbrack 0,1\rbrack$.