State with reason whether following functions have inverse f : {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}

Question

Philoid · Accepted Answer

It is given that f : {1, 2, 3, 4} → {10} with

f = {(1, 10), (2, 10), (3, 10), (4, 10)}

From the given definition of f,

We can see that f is a many one function as:

f(1) = f(2) = f(3) = f(4) = 10

= > f is not one-one.

Therefore, function f does not have an inverse.