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With a non-zero number, the following operations are allowed: x1+xx, x1xx. Is it true that from every non-zero rational number one can obtain each rational number with the help of a finite number of such operations?

An iterative polyline serves as a geometric interpretation of the iteration process. To construct it, on the Oxy plane, the graph of the function f(x) is drawn and the bisector of the coordinate angle is drawn, as is the straight line y=x. Then on the graph of the function the points A0(x0,f(x0)),A1(x1,f(x1)),,An(xn,f(xn)), are noted and on the bisector of the coordinate angle – the points B0(x0,x0),B1(x1,x1),,Bn(xn,xn),. The polygonal line B0A0B1A1BnAn is called iterative.

Construct an iterative polyline from the following information:

a) f(x)=1+x/2, x0=0, x0=8;

b) f(x)=1/x, x0=2;

c) f(x)=2x1, x0=0, x0=1,125;

d) f(x)=3x/2+6, x0=5/2;

e) f(x)=x2+3x3, x0=1, x0=0,99, x0=1,01;

f) f(x)=1+x, x0=0, x0=8;

g) f(x)=x3/35x2/x+25x/6+3, x0=3.