Mathematics - Functions Question with Solution | TestHub

$f\left(x\right)+2. f\left(\frac{1}{x}\right)=3x \dots \left(1\right)$

Replace$x$by$\frac{1}{x}$, we get

$f\left(\frac{1}{x}\right)+2f\left(x\right)=\frac{3}{x} \dots \left(2\right)$

From$\left(1\right)$and$\left(2\right)$

$3f\left(x\right)=\frac{6}{x}-3x$

$f\left(x\right)=\frac{2}{x}-x$

$\because$$f\left(x\right)=f\left(-x\right)$

Therefore$\frac{2}{x}-x= -\frac{2}{x}+x$

$\Rightarrow \frac{4}{x}=2x$

$\Rightarrow 2=x^2$

$\Rightarrow x= \pm \sqrt{2}$

Contains exactly two elements