Question

In Lecture 13 (Newton's Method), what is the intuition for changing the problem of x^2 = 5 to
f(x) = x^2 - 5? I don't understand why we change a number into a function.

Answer 1

because the function you just defined gives you the solutions when solving for y=0. By solutions i mean the the two numbers which, if squared, give you 5

Answer 2

Newton's method give you solution to equations of the type f(x) = 0, so we have to change the equation x^2 = 5 to this form, thus we subtract 5 from both side, yielding x^2 - 5 = 0, and we call it f(x).