Let X and Y be sets and f : x → y be one-one and onto function, then the true statement is:

Concept:  

A function f: A→ B is defined to be injective or one-one if every value of f(x) is different for different values of x.

If the above condition is not satisfied, then the function is called many-one.

A function f: A→ B is defined to be surjective or onto if for every value of f(x), there will be a value  x that will exist.

Explanation:

Given:

Let A be a set having elements {a, b, c, d, e}.

Let f: A→ B is a function defined such that it is one-one and onto.

The set B will have a single value of f(x) for each value of x in A since the function is one-one.

Let the corresponding elements be {1, 2, 3, 4, 5} in B against {a, b, c, d, e} in A.

Since the function is onto, each value in B will have a corresponding value in x. Hence, there will be no more elements in B other than {1, 2, 3, 4, 5}.

The inverse of the function will be f^--1: B→ A.

⇒ As per the discussion above A =  {a, b, c, d, e} and B = {1, 2, 3, 4, 5}.

⇒ We can see that for every element in B, there is a corresponding element in A.

⇒ it can be said that f^--1 is one-one and onto.

Hence the correct answer is option 4.