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  4. Domain of f(x) = √ log (2x-x2) is

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Q. Domain of $f(x) = \sqrt{\log (2x-x^2)}$ is

Relations and Functions

Solution:

$f(x) $ will be real if $\log (2x - x^2) \geq 0$
$\Rightarrow 2x -x^2 \ge e^\circ = 1$
$\Rightarrow x^2- 2x + 1 \le 0 $
$\Rightarrow (x - 1)^2 \le 0 $
$ \Rightarrow (x - 1)^2 = 0 $
$ \Rightarrow x = 1 $
$\therefore \,D_f = \left\{1\right\}$.