Explanation:

To determine whether the composition of two functions, g o f, is one-one, we need to understand the properties of one-one functions.

One-One Functions:
A function is said to be one-one (or injective) if each element of the domain is mapped to a distinct element in the codomain. In other words, for every pair of elements a and b in the domain of the function, if f(a) = f(b), then a = b.

Composition of Functions:
The composition of two functions, g o f, is a function obtained by applying the function f first and then applying the function g. Mathematically, (g o f)(x) = g(f(x)).

Properties of Composition of One-One Functions:
When the composition of two functions is considered, the following properties hold true:
1. If f and g are both one-one functions, then g o f is also one-one.
2. If f is a one-one function and g is an onto function, then g o f is also one-one.

Explanation of the correct answer:
In the given question, it is mentioned that f and g are two one-one functions. Therefore, according to property 1 mentioned above, the composition g o f will also be one-one.

Explanation of incorrect options:
a) Bijective function: A bijective function is both one-one and onto. Since the question only specifies that f and g are one-one functions, we cannot conclude that g o f is a bijective function.
c) Many-one function: A many-one function is a function where different elements of the domain can be mapped to the same element in the codomain. Since f and g are both one-one functions, it implies that g o f cannot be a many-one function.
d) Many-one and onto function: The composition of two one-one functions cannot be many-one and onto at the same time. Therefore, this option is incorrect.

Therefore, the correct answer is option 'A' - g o f is a one-one function.