$1.$ Define functions $(15)$

f$($x$)=$ rx$(1$ x$)$

g$($x$)=$ f$($f$($x$)).$

The equation

x $=$ g$($x$)$

can be solved using fixed$-$point iteration method with an initial value x$0=0\mathrm{.}5.$ Write

a computer program which solve x multiple times for r $=0,0\mathrm{.}01,0\mathrm{.}02,...,3\mathrm{.}30$ with a

tolerance $106$

$.$ Submit the program and a plot of x against r$.$