f:[1,∞)→[2,∞)  is given by f(x)=x+1/x , then f−1(x)  equals

f:[1,∞)→[2,∞) ; f(x)=x+1/x                                                                                f(x)=x+1/x In the interval [1,∞) , f(x)  is one-one and Rf=[2,∞) ∴  f  is one-one, onto.y=x+1x ⇒ x2−xy=1=0 ⇒ x=y±y2−42 Since x≥1  for all y≥2 f−1(y)=x=y+y2−42 ⇒ f−1(x)=x+(x2−4)2 .