The x intercept(s) can be found by putting f(x)=0, so x=2cosx. This needs to be solved using a calculator and trial and error. If x is in radians, then the solution (intercept) is 1.02987 approx. This is 59.01 degrees as an angle.
[The method I used on my calculator was to make sure that angles would be in radians rather than degrees. Then I put in the function x-2cosx and calculated the value of this expression in the range x=0 to 1.5. The calculator tabulated the results and showed that the function went from negative to positive between x=1.0 and 1.1, so I refined the resolution to evaluate the function between these values and discovered a sign change between x=1.02 and 1.03. I continued to refine the resolution to the next decimal place and ended up with the value above as an approximation. The function is very close to zero at x=1.02987. To convert from radians to degrees for the purpose of evaluating the cosine I multiplied the value of x by 180/(pi)=57.296 (1 radian=57.296 degrees).]