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Mark (√) against the correct answer in the following:

Question:

Mark (√) against the correct answer in the following:

Let $f(x)=\sqrt{\log }\left(2 x-x^{2}\right) .$ Then, dom $(f)=?$

A. $(0,2)$

B. $[1,2]$

C. $(-\infty, 1]$

D. None of these

 

Solution:

$f(x)=\sqrt{\log }\left(2 x-x^{2}\right)$

$2 x-x^{2}>1$

$\Rightarrow x^{2}-2 x+1<0$

$\Rightarrow(x-1)^{2}<0$

$\Rightarrow x-1<0$

$\Rightarrow x<1$

$\log \left(2 x-x^{2}\right)>0$

$\Rightarrow 2 x-x^{2}>e^{0}=1$

$\Rightarrow x<1$

$\operatorname{Dom}(f)=(-\infty, 1)$

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