Problem Statement

{2,4,6}
2*4
4*4

Determine a domain on which f−1 exists, and find a formula for f−1 for this domain of f.

 
Step 1

Question Sequence

Question 1

The inverse function, f-1(x) exists if and only if f(x).

Incorrect
Correct

 
Step 2

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.

Question Sequence

Question 3

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.

2
Incorrect
Correct

 
Step 3

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.

Question Sequence

Question 6

Solve for x in the restricted domain of f, x ≥ 4.

Solve for x in the restricted domain of f, x ≤ 4.

Where a = .

Correct.
Incorrect.