Question

Write the pre – images of 2 and 3 in the function, f = {(12, 2), (13, 3), (15, 3), (14, 2), (17, 17)}.

Answer 1

Hint: Consider (x, y) as coordinate y = 2 and y = 3 are given. Now the pre – image of y = 2 and y = 3 is the value of x corresponding to it. Thus write down the numbers.

Complete step by step solution:
We have been given a function f. Each element of a given subset A of its domain produces a set called the “image of A under f”.
If x is a number of X, then f (x) = y is the image of X under f. y is alternatively known as the output of f for argument x.
Here we are asked to find the pre – image of 2 and 3 in the given function. We can represent a coordinate as (x, y). If we take y = 2 and y = 3, we need to find the pre – image from the given function f.
f = {(12, 2), (13, 3), (15, 3), (14, 2), (17, 17)}
Let us take the first term (12, 2). We have y = 2 hence the pre – image is x = 12.
Now for the next term (13, 3). We have y = 3 hence the pre – image is x = 13.
For the next coordinate (15, 3). We have y = 2, hence the pre – image is x = 15.
For the coordinate (14, 2). We have y = 2, hence the pre – image as x = 14.
For (17, 17) we can’t find any pre - image as we are asked to find the pre – image of 2 and 3 in the function. Thus we get 12, 13, 15 and 14 as the pre – image of the given function.

Note: Pre – image has nothing to do with the inverse of the function f. Pre – image occurs in a variety of subjects, the most persistent of their map which continue by definition, if pre – image of every open set is open.