Final answer:
The equation 2cos(x) = 4 does not have any solutions because the value of the cosine function is constrained between -1 and 1, and cannot equal 2.
Step-by-step explanation:
The equation given is 2cos(x) = 4, which we need to solve over the interval {0, 2π}. To find the values of x that satisfy this equation, we first simplify the equation:
cos(x) = 2
This equation does not have a solution because the cosine function has a range of [-1, 1], and no real number x will result in cos(x) having a value of 2. Therefore, there are no solutions to this equation within the given interval, or any interval, because the cosine function cannot reach a value of 2.
Detailed Solution
The cosine function oscillates between -1 and 1, and any value outside this range is not possible. For a valid solution, the right side of the equation would have to be between -1 and 1 inclusive. As the right side of the given equation is 2, which is outside the range of cosine, this equation has no solution.