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  4. The domain of definition of the function f(x)=√ log 10((5 x-x2/4)) is

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Q. The domain of definition of the function $f(x)=\sqrt{\log _{10}\left(\frac{5 x-x^{2}}{4}\right)}$ is

AIEEEAIEEE 2002Inverse Trigonometric Functions

Solution:

$\because f(x)=\sqrt{\log _{10}\left(\frac{5 x-x^{2}}{4}\right)}$
$\therefore f(x)$ exists only for
$\Rightarrow $
$\log _{10}\left(\frac{5 x-x^{2}}{4}\right) \geq 0$
$\frac{5 x-x^{2}}{4} \geq 1$
$\Rightarrow x^{2}-5 x+4 \leq 0$
$\Rightarrow (x-1)(x-4) \leq 0 $
$\Rightarrow x \in[1,4]$