The domain of the function f(x) = x - x^2 + 4 + x + 4 - x is - Vidyadip

MCQ

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

A
$[ - 4,\;\infty )$
B
$[-4, 4]$
C
$[0, 4]$
✓
$[0, 1]$

✓

Answer

Correct option: D.

$[0, 1]$

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

Clearly $f(x)$ is defined, if $4 + x \ge 0$ ==> $x \ge - 4$

$4 - x \ge 0$ ==> $x \le 4$

$x(1 - x) \ge 0$ ==> $x \ge 0$ and $x \le 1$

$\therefore$ Domain of $f = ( - \infty ,\,4] \cap [ - 4,\,\infty ) \cap [0,\,1]$$ = [0,\,1]$.

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