$($with python$)$ Your homework is to write a program, which will find a root of function that taken from user with input method by using Fixed$-$Point Iteration Method.

This method is a iterative process for finding an approximation to a root of a function by repeatedly applying a transformation of that function, starting from an initial guess, until the process converges to a fixed point. $($ You should get x$0,$ F$($x$)$ and max iteration number and tolerance from user$)$ But program should find g$($x$)$ itself.

Your program should use the following inputs:

f$($x$)$: The function to find its root

x$\_0$: The initial guess for iterative process

tol: A value, which is very close to zero, to stop the iterations

max$\_$iter: The maximum number of iterations

Your program should satisfy the following requirements:

To find the transformed function for f$($x$)=0->$ x$=$g$($x$)$

To converge to a root with iterations x$\_($n$+1)=$g$($x$\_$n$)$

To stop if $|$f$($x$\_$n$)|$max$\_$iter

To have a visual representation of the iterative process, like an animation on a plot

To get the inputs as JSON and response as JSON, so run as an API

To have an independent GUI to use this API