Question

If $f$ is a continuous function on the real line. Given that $x^2+\left(f\right(x)-2)x-\sqrt{3}.f\left(x\right)+2\sqrt{3}-3=0$. Then the value of $f\left(\sqrt{3}\right)$

• A. can not be determined
• B. $2(1-\sqrt{3}$
• C. $zero$
• D. $\frac{2(\sqrt{3}-2)}{\sqrt{3}}$

Answer 1

The correct option is A can not be determined

Given $f\left(x\right)$ is a continuous function on the real line.

Since, $\sqrt{3}$ lies on the real line, then the given equation will hold for $x=\sqrt{3}$ also.

Then we will have

$(\sqrt{3}{)}^2+(f\left(\sqrt{3}\right)-2)\sqrt{3}-\sqrt{3}.f(\sqrt{3})+2\sqrt{3}-3$

$=0$.

So, the given equation is an identity. Which is true for all real $x$.

So, $f\left(\sqrt{3}\right)$ can not be determined from the given equation.