The domain of the function -log 0-5 x isA- 0- -B- 0-1-C- 0-5-1D- 1- -

The correct option is B (0,1]By definition of log x, x gt;0 and also log_0.5 x≥ 0 ∴ x≤ 1 as in above question, base being less than 1; domain is (0,1]. ...

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Standard XI

Mathematics

Conditions on the Parameters of Logarithm Function

The domain of...

Question

The domain of the function $\sqrt{(l o g_{0.5} x)}$ is

(1, \infty)

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(0, \infty)

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(0, 1]

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(0.5, 1)

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Solution

The correct option is C $(0, 1]$
By definition of $l o g x, x > 0$ and also $l o g_{0.5} x \geq 0$
$∴ x \leq 1$ as in above question, base being less than 1;
domain is (0,1].

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The domain of the function √(log0.5 x) is

The correct option is C (0,1]By definition of log x,x>0 and also log0.5 x≥0 ∴ x≤1 as in above question, base being less than 1; domain is (0,1].

The domain of the function $\sqrt{(l o g_{0.5} x)}$ is

The correct option is C $(0, 1]$
By definition of $l o g x, x > 0$ and also $l o g_{0.5} x \geq 0$
$∴ x \leq 1$ as in above question, base being less than 1;
domain is (0,1].