What Are the 4 Types of Functions?

The four main types of functions based on mapping are: one-one (injective), onto (surjective), bijective (both one-one and onto), and many-one functions.

1. One-One Function (Injective):

• Each element in codomain has at most one pre-image
• Different inputs → different outputs
• Example: f(x) = 2x

2. Onto Function (Surjective):

• Every element in codomain has at least one pre-image
• Range = Codomain
• Example: f(x) = x³ from R to R

3. Bijective Function:

• Both one-one AND onto
• Perfect pairing between domain and codomain
• Has an inverse function
• Example: f(x) = x + 5

4. Many-One Function:

• Multiple domain elements map to same codomain element
• Example: f(x) = x² (both 2 and -2 map to 4)

Alternative Classification: Functions can also be categorized as: linear, quadratic, polynomial, exponential, logarithmic, trigonometric, etc.