∫y = f(x) The coordinate (x, y) of any point on the image satisfies the equation lg(x+y)=lg(x)+lg(y).

∴x,y>0

lg(x+y)=lgx+lgy=lgxy

∴x+y=xy

When 0 < x ≤ 1, x+y=xy≤y, which is not true.

∴x> 1

∴y=x/(x- 1)= 1+ 1/(x- 1)

Obviously, y=f(x) is a decreasing function on the interval (1,+infinity).

x+y = x+ 1+ 1/(x- 1)= x- 1+ 1/(x- 1)+2≥2 √( x- 1)× 1/(x- 1)+2 = 4

∴x+y≥4