The domain of an inverse function is the range of the original function.
Question
The domain of an inverse function is the range of the original function.
Solution
The domain of an inverse function is the range of the original function.
To understand this concept step by step, let's break it down:
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Start with the original function. The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.
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The range of a function, on the other hand, refers to the set of all possible output values, or y-values, that the function can produce.
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Now, consider the inverse function. The inverse function essentially swaps the roles of the input and output values. In other words, if the original function takes an x-value as input and produces a corresponding y-value as output, the inverse function takes that y-value as input and produces the original x-value as output.
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Since the inverse function swaps the roles of input and output, the domain of the inverse function will be the set of all possible output values, or y-values, of the original function. This is because these y-values will now serve as the input values for the inverse function.
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Therefore, the domain of the inverse function is equal to the range of the original function.
In summary, the domain of an inverse function is the range of the original function.
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