Algebra-2

To find the domain and range of the inverse function for the function , we first need to analyze the original function.

Step 1: Identify the Domain and Range of

1. Domain of :

The function is a quadratic function.

Quadratic functions are defined for all real numbers.

Therefore, the domain is: Domain of .

2. Range of :

Since is always non-negative and multiplied by -2 and then 6 is subtracted, the maximum value of is 6.

As varies over all real numbers, will take on values less than or equal to 6.

Thus, the range is: Range of

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