Question

consider the sets A={1,2,3,4, 5} ,B={1,4,9,16,25} and a function F:A → B defined by f(1) = 1,f(2) = 4,f(3) = 9,f(4) = 16,f(5) = 25
(a) show that f is one -one and onto
(b) does f^-1 exists ?? (Inverse)

Answer 1

Answer:

a) the set is one-one as each of the elements of set B are a function of set A. For onto each of the elements of set A should at least have one function. Therefore the given function is one-one and onto.

b) since the given function is one-one and onto f inverse exist