Question

{(3, 1), (4, -3), (8, -3)}
Find the inverse function.

Answer 1

Step-by-step explanation:

3 if x=1

4 if x=−3

8 if x=−3

Please note that this is a piecewise-defined function because the same y value (-3) is associated with two different x values (4 and 8).

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Answer 2

The inverse of the set {(3, 1), (4, -3), (8, -3)} by swapping x and y is {(1, 3), (-3, 4), (-3, 8)}, but since two pairs have the same 'y' after swapping, the original function is not one-to-one and does not have an actual inverse function.

Step-by-step explanation:

The question involves finding the inverse function of a given set of ordered pairs.

To find the inverse, we swap the x and y values in each pair. The original set is {(3, 1), (4, -3), (8, -3)}. After swapping, we obtain the inverse set, which is: {(1, 3), (-3, 4), (-3, 8)}. This represents the inverse relation, and if plotted, would be the reflection of the original function across the line y=x. In this case, since two pairs have the same y value after swapping (-3), the original function is not one-to-one and does not have an inverse function; we've only described its inverse relation.

To find the inverse function, we need to switch the x and y values in each ordered pair and solve for y.

Given the ordered pairs (3, 1), (4, -3), and (8, -3), the inverse function would be:

(1, 3)

(-3, 4)

(-3, 8)

So, the inverse function is y = 3x - 8.