Final answer:
The question seeks to solve an equation using fixed-point iteration given parameters, but the exact equation is missing. Without the specific equation, it's not possible to write the program to find x. Fixed-point iteration relies on iterative calculations from an initial guess until convergence.
Step-by-step explanation:
Solving for x in Fixed-Point Iteration
To solve for the variable x using two different fixed-point iteration functions given p = 3 and k = 0.05, we need the exact equation to apply the method. However, based on the provided context, it seems we do not have the complete equation to proceed.
For a typical fixed-point iteration, you would rearrange the equation such that x equals some function of x (e.g., x = g(x)), then iteratively plug the output back as the input until x converges to a stable value. An example of a fixed-point iteration function could be x = cos(x), but without the specific equation, it is not possible to give a precise answer.
Fixed-point iteration methods are often used in numerical analysis to find solutions to equations where algebraic manipulation is challenging. The concept relies on an iterative process and a suitable initial guess where the results converge towards a solution over successive iterations. Careful selection of the function g(x) is crucial to ensure convergence.
It appears there has been a typo or misunderstanding in the formulation of the question as key information seems to be missing, making it impossible to write a program to solve the equation as requested.