If fx-sinlog-4-x2-1-x- then the domain of fx is

The correct option is B ( 2,1) Given, f(x) = sin log( √(4 x^2)/1 x ) For domain, √(4 x^2)/1 x gt; 0, and 1 x ≠ 0 ⇒ (1 x) gt;0 and 4 x^2 gt;0 ⇒ x lt ...

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Byju's Answer

Standard XI

Mathematics

Domain

If fx=sinlog√...

Question

If f(x) = sin log $(\frac{\sqrt{4 - x^{2}}}{1 - x})$ , then the domain of f(x) is ___

$(1, 2)$

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$(- 2, 1)$

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$(- 1, 2)$

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$(0, 2)$

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Solution

The correct option is B
$(- 2, 1)$

Given, f(x) = sin log $(\frac{\sqrt{4 - x^{2}}}{1 - x})$
For domain, $\frac{\sqrt{4 - x^{2}}}{1 - x} > 0, a n d 1 - x \neq 0 \Rightarrow (1 - x) > 0 a n d 4 - x^{2} > 0 \Rightarrow x < 1 a n d | x | < 2 \Rightarrow - 2 < x < 1$
Thus, domain $ϵ$ (-2, 1)

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If f(x) = sin log $(\frac{\sqrt{4 - x^{2}}}{1 - x})$ , then the domain of f(x) is ___

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If f(x) = sin log (√4−x21−x), then the domain of f(x) is ___

The correct option is B (−2,1) Given, f(x) = sin log(√4−x21−x) For domain, √4−x21−x>0, and 1−x≠0⇒ (1−x)>0 and 4−x2>0⇒ x<1 and |x|<2⇒−2<x<1 Thus, domain ϵ (-2, 1)

If f(x) = sin log $(\frac{\sqrt{4 - x^{2}}}{1 - x})$ , then the domain of f(x) is ___

The correct option is B
$(- 2, 1)$

Given, f(x) = sin log $(\frac{\sqrt{4 - x^{2}}}{1 - x})$
For domain, $\frac{\sqrt{4 - x^{2}}}{1 - x} > 0, a n d 1 - x \neq 0 \Rightarrow (1 - x) > 0 a n d 4 - x^{2} > 0 \Rightarrow x < 1 a n d | x | < 2 \Rightarrow - 2 < x < 1$
Thus, domain $ϵ$ (-2, 1)