Question

The mapping diagram shows a function S(x).

Which mapping diagram shows the inverse of S(x)?

Answer 1

Again the domain consists of the pre-images and the range the images.

When we are looking for the f(x) we just look at the number it is pointing to in the range (when we have a diagram), and when we are looking for x when f(x)=y we look at the number that has a line pointed to y.

So the f(4)=

f(x)=4 when x is 8

Answer 2

The diagram where the numbers on the left (3, 2, 1, 0) are now on the right, each mapping to its corresponding number from the original function (5, 4, 3, 2) on the left.

Option A.

To find the inverse of a function from a mapping diagram, here's what you should do:

1. Identify the Pairs in the Original Function: Look at the mapping diagram for the function S(x) and write down the pairs. Each element from the first set (the domain) is associated with an element from the second set (the range).

2. Swap the Pairs for the Inverse: For the inverse function, each element from the range (second set in the original function) will become an element in the domain (first set in the inverse function) and vice versa.

3. Create the Inverse Mapping Diagram: Draw a new mapping diagram with the swapped pairs. This will show the inverse function.

Now, let's apply these steps to the given diagram. The original function pairs are as follows:

- 5 maps to 3

- 4 maps to 2

- 3 maps to 1

- 2 maps to 0

For the inverse function, we swap these pairs, resulting in:

- 3 maps to 5

- 2 maps to 4

- 1 maps to 3

- 0 maps to 2