For the given function fx one possible start value x0 0

Question

Consider the function,

f(x)=cos(2x)+(3/2)x-1 which has exactly one root a = 0.

a) For the given function f(x), one possible start value x₀ =/= 0 for Newton's method shall be determined so that the root a = 0 can be found exactly with one iteration only. Turn this problem into a root finding problem of the form g(x) = 0 with unknown root a = x₀.