Your homework is to write a program, which will find a root of any function 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.

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)|
• To stop if 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 GET FUNCTON FROM USER WTH NPUT AND MAKE PYTHON ( IT IS SGNFCANT)