Determine a domain on which f−1 exists, and find a formula for f−1 for this domain of f.
The inverse function, f-1(x) exists if and only if f(x).
Since f(x) is not one-to-one, it is not invertible. However, we can restrict the domain to one where f(x) is one-to-one and hence f(x) will be invertible on that domain.
Given any parabola, if we restrict the domain to only those numbers to the right (or left) of the vertex, then by the horizontal line test, the function be one-to-one and hence invertible.
Now that we have a domain on which f(x) is invertible, let's find a formula for f−1(x). To do so, solve y = f(x) for x in terms of y.
There can only be one inverse function and it depends on the restricted domain of f.
Solve for x in the restricted domain of f, x ≥ 4.
Solve for x in the restricted domain of f, x ≤ 4.
Where a = .