Let A = {2, 3, 4, 5} and B = {7, 9, 11, 13}, and

let f = {(2, 7), (3, 9), (4, 11), (5, 13)}.


Show that f is invertible and find f-1.


To Show: that f is invertible


To Find: Inverse of f


[NOTE: Any functions is invertible if and only if it is bijective functions (i.e. one-one and onto)]


one-one function: A function f : A B is said to be a one-one function or injective mapping if different elements of A have different images in B. Thus for xl, x2 A & f(x1), f(x2) B, f(x1) = f(x2) x1= x2 or x1 x2f(x1) f(x2)


onto function: If range = co-domain then f(x) is onto functions.


So, We need to prove that the given function is one-one and onto.



As we see that inthe above figure (2 is mapped with 7), (3 is mapped with 9), (4 is mapped with 11),


(5 is mapped with 13)


So it is one-one functions.


Now elements of B are known as co-domain. Also, a range of a function is also the elements of B(by definition)


So it is onto functions.


Hence Proved that f is invertible.


Now, We know that if f : A B then f-1 : B A (if it is invertible)


So,



So f-1 = {(7, 2), (9, 3), (11, 4), (13, 5)}


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