Final answer:
The range of the inverse function of 5 sin x + 2 is [-3, 7] because after the transformation applied, the minimum and maximum possible values of the original function are -3 and 7 respectively.
Step-by-step explanation:
The question you're asking about the range of the inverse function relates to a specific mathematical concept. The original function in question is 5 sin x + 2, and we are looking for the range of its inverse function. The sine function oscillates between -1 and +1, so after applying the transformation implied by multiplying by 5 and adding 2, the new range of the function becomes the interval [-3, 7]. This is because the minimum value is -5 + 2 = -3 and the maximum value is 5 + 2 = 7. However, the domain of the sine function, and consequently its inverse, is indeed all real numbers. But in this case, the range is specifically [-3, 7] due to the transformation applied to the sine function.