What is the inverse of this function?

Step-by-step explanation:

The Inverse of a Function

Given a function f(x), the inverse of f, called is a function that satisfies:

The domain of f becomes the range of its inverse and vice-versa.

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

* Solve the equation for x.

* Swap the variables

We are given the function:

Defined in the interval x ≥ -3

Note f is always negative, thus its range is f(x) ≤ 0

Now we find the inverse. Call y=f(x):

Multiplying by 2:

Squaring both sides:

Subtracting 3:

Swapping variables:

Thus:

The domain of the inverse is the range of f, thus x is restricted to

x ≤ 0

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step-by-step explanation: