posted by sam .
Find all solutions to the equation
2cos(2x) = x + 1, correct to 4 decimal places.
2 cos(2x) never gets out of the range [-2,2]
So, whenever |x+1| > 2, there are no solutions.
That means all solutions are in [-3,1]
A little Newton-Raphson should work nicely here, or a bisection method.