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Why is the range [-3, 7] for the inverse of 5 sin x + 2? Is it because the inverse's domain appears to be all real numbers?

User EFernandes
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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.

User Chrissr
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