First slide

Continuity

Question

$If f (x) be a continuous function for all real values of x and satisfies$ $x^{2} + x (f (x) - 2) + 2 \sqrt{3} - 3 - \sqrt{3} f (x) = 0 \forall x \in R then the value of f (\sqrt{3}) is$

Moderate

A

$\sqrt{3}$
B

$2 (\sqrt{3} - 1)$
C

$2 \sqrt{3} - 1$
D

$2 (1 - \sqrt{3})$

Solution

$f (\sqrt{3}) = \underset{x \to \sqrt{3}}{L t} \frac{x^{2} + 2 x + 2 \sqrt{3} - 3}{\sqrt{3} - x} = 2 (1 - \sqrt{3})$

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