Question

If 2f (x) − $$3f\left(\frac{1}{x}\right)=x^2$$ (x ≠ 0), then f(2) is equal to

 

विकल्प

• (a)  $$-\frac{7}{4}$$

   

• (b)  $$\frac{5}{2}$$

   

• (c) −1

• (d) None of these

   

Answer 1

(a)  $$-\frac{7}{4}$$

2f (x) − $$3f\left(\frac{1}{x}\right)=x^2$$  (x ≠ 0)                  ....(1)

$$\text{ Replacing x by }\frac{1}{x}:$$
$$2f\left(\frac{1}{x}\right)-3f(x)=\frac{1}{x^2}...(2)$$
$$\text{ Solving equations (1) \& (2) }$$
$$-5f(x)=\frac{3}{x^2}+2x^2$$
$$\Rightarrow f(x)=\frac{-1}{5}(\frac{3}{x^2}+2x^2)$$
$$\text{ Thus },f(2)=\frac{-1}{5}(\frac{3}{4}+2\times 4)$$
$$=\frac{-1}{5}\left(\frac{3+32}{4}\right)$$
$$=\frac{-7}{4}$$