Question

If f and g are one-to-one functions, it follows that

g is one-to-one. Justify your answer.

a) True
b) False

Answer 1

The statement is true. If f is one-to-one, g must also be one-to-one.The correct option is A.

Step-by-step explanation:

The statement given is true. If function f is one-to-one, it means that every element in the domain maps to a unique element in the codomain. Now, if we have another function g, and assume g is not one-to-one, it means that there exist two distinct elements from the codomain that are mapped to the same element in the domain. However, if g is not one-to-one, then f(g(x)) cannot be one-to-one, since there will exist at least one element in the domain that maps to two distinct elements in the codomain, violating the definition of a one-to-one function.