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If  f(x) be continuous function for all x and satisfies

\mathrm{x}^{2}+(\mathrm{f}(\mathrm{x})-2) \mathrm{x}-2 \sqrt{3}+3-\sqrt{3} \,\,\mathrm{f}(\mathrm{x})=0 \,\,\, \forall \mathrm{x} \in \mathrm{R}, then \mathrm{f}(\sqrt{3}) is equal to 

Option: 1

Zero


Option: 2

2\left(1-\frac{2}{\sqrt{3}}\right)


Option: 3

2(1-\sqrt{3})


Option: 4

None of these


Answers (1)

best_answer

f(x)=\frac{x^2-2 x+2 \sqrt{3}-3}{\sqrt{3}-x}, x \neq \sqrt{3}

\lim _{x \rightarrow \sqrt{3}} f(x)=\lim _{x \rightarrow \sqrt{3}} \frac{x^2-2 x+2 \sqrt{3}-3}{(\sqrt{3}-x)} \\

=\lim _{x \rightarrow \sqrt{3}}(2-\sqrt{3}-x)=2(1-\sqrt{3}) \\

 \Rightarrow f(\sqrt{3})=2(1-\sqrt{3})

as f(x) is continuous.

Posted by

Riya

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