Answer:
The equation has at least one solution if and only if 1 ≤ k ≤ 3.
Step-by-step explanation:
The equation sin(x) = 2 - k, with 0 ≤ x ≤ π, has at least one solution if and only if the value of (2 - k) lies within the range of the sine function, which is -1 to 1.
Since the range of the sine function is from -1 to 1, for the equation sin(x) = 2 - k to have at least one solution, the value of (2 - k) must fall within this range. Therefore, the condition for the equation to have at least one solution is:
-1 ≤ 2 - k ≤ 1
By solving the inequality, we get:
2 - 1 ≤ k ≤ 2 + 1
1 ≤ k ≤ 3
So, the equation sin(x) = 2 - k has at least one solution if and only if k lies within the range of 1 to 3.
Therefore, the correct answer is: The equation has at least one solution if and only if 1 ≤ k ≤ 3.
