Assignment:
Let X be a metric space and x0 in X. Define a function f: X --> R (all real numbers) by f(x) = d(x,x0). Show that f is continuous.
HINT: Prove the variant of the triangle inequality which says |d(x,z)-d(y,z)|< d(x,y) for any x,y,z in X
Provide complete and step by step solution for the question and show calculations and use formulas.