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 f(x)

1.Domain of f(x):

The function is a quadratic function, which is defined for all real numbers.

Therefore, the domain is:

Domain of

2.Range of f(x):

To find the range, we note that this is a parabola opening upwards (since the coefficient of is positive).

The vertex of the parabola can be found using the formula for the vertex of a parabola , which occurs at . Here a = 2 and b = 0, so:

Now, substitute x = 0 back into f(x) to find the minimum value:

Thus, the minimum value of f(x) is -4. Therefore, the range is:

Range of

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