Give an example of a function fx such that fx is injective b

Give an example of a function f(x) such that f(x) is injective but its component functions f1(x) and f2(x) are not injective.

f(x) = (f1(x), f2(x))

Solution

A function is said to be injective(one-one) function if the eleements of set A have unique images in set B.

to show that a function is injective we assume that x1 and x2 of A with f(x1)=f(x2)

we can give an example of a function f(x)=x³ as a set which is injective but its components are not injective

for the function defined let f be a mapping from a set of integers to integers that is

f:Z->Z