A function is said to be ______________ if and only if f(a) = f(b) implies that a = b for all a and b in the domain of f. one-to-many one-to-one many-to-many many-to-one
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A function is said to be one-to-one if and only if f(a) = f(b) implies that a = b.
The domain, range, and function expression are used to define the different sorts of functions.
Based on the number of connections between the components in the domain and the codomain, various functions can be categorized based on a set of set elements.
Following are the several categories of functions based on a collection of elements.
- One-to-one function: The definition of a one-to-one function is f: A → B, where each element in set A is linked to a unique element in set B.
- Many-to-one function: The function f: A → B, which connects multiple elements of the set A to the same element in the set B, defines a many-to-one function.
- Onto function: Every element in set B has a pre-image in set A for a function defined by f: A → B.
- Bijective function: These are the functions that are both one-to-one and onto.
- Into function: These functions could be defined as the exact opposite of an onto function.
- Constant function: f(x) = K, where K is a real number, is the formula for the constant function.
Therefore, the correct answer here is a one-to-one function.
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