Let f be a function satisfying $2 f(x)-3 f\left(\frac{1}{x} ight)=x^2$ for any $x
eq 0$. Then $f(

Question

Let f be a function satisfying $2 f(x)-3 f\left(\frac{1}{x}ight)=x^2$ for any $x 
eq 0$. Then $f(2)$ is

Professor PC Thomas Classes · Answer

$2 f(2)-3 f\left(\frac{1}{2}ight)=4$ ...(1)
$2 \mathrm{f}\left(\frac{1}{2}ight)-3 \mathrm{f}(2)=\frac{1}{4}$ ...(2)
$(1) 	imes 2 \Rightarrow 4 \mathrm{f}(2)-\mathrm{ff}\left(\frac{1}{2}ight)=8$
$(2) 	imes 3 \Rightarrow 6 \mathrm{f}\left(\frac{1}{2}ight)-9 \mathrm{f}(2)=\frac{3}{4} \quad$ Adding
$-5 f(2)=8+\frac{3}{4}=\frac{35}{4} \Rightarrow f(2)=-\frac{7}{4}$