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  • If f(x) be continuous function for all x and satisfies <img alt="x^2+(f(x)-2) x-2 \sqrt{3}+3-\sqrt{3} f(x)=0 \forall x \in R" src="https://entrancecorner.oncodecogs.com/gif.latex?x%5E2&plu

If f(x) be continuous function for all x and satisfies x^2+(f(x)-2) x-2 \sqrt{3}+3-\sqrt{3} f(x)=0 \forall x \in R, then 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

\begin{aligned} & 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 \quad f(\sqrt{3})=2(1-\sqrt{3}) \end{aligned}\\ \text{as f(x) is continuous.}

Posted by

Devendra Khairwa

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