fx+1x=x2+1x2fx+1x=x2+1x2+2-2fx+1x=x2+1x2+2 × x × 1x-2fx+1x=x2+1x2+2 × x × 1x-2fx+1x=x+1x2-2Replace x+1x by y fy=y2-2Now replace y by xfx=x2-2

Plz solve question 1.

f (x + \frac{1}{x}) = x^{2} + \frac{1}{x^{2}} f (x + \frac{1}{x}) = x^{2} + \frac{1}{x^{2}} + 2 - 2 f (x + \frac{1}{x}) = x^{2} + \frac{1}{x^{2}} + 2 \times x \times \frac{1}{x} - 2 f (x + \frac{1}{x}) = (x^{2} + \frac{1}{x^{2}} + 2 \times x \times \frac{1}{x}) - 2 f (x + \frac{1}{x}) = {(x + \frac{1}{x})}^{2} - 2 R e p l a c e (x + \frac{1}{x}) b y y f (y) = y^{2} - 2 N o w r e p l a c e y b y x f (x) = x^{2} - 2