Conclusion – Classes of Functions

What is a Function?

A function f from a set A to a set B is a rule that assigns each element a ∈ A exactly one element b ∈ B. This is denoted as f : A→B...

Terms Related to Functions

Domain and co-domain – If f is a function from set A to set B, then A is called Domain, and B is called co-domain. Range – Range of f is the set of all images of elements of A. Basically Range is a subset of co-domain. Image and Pre-Image – b is the image of a and a is the pre-image of b if f(a) = b....

Classes of Functions

1. Injective Functions (One-to-One)...

Composition of Functions

Let g be a function from B to C and f be a function from A to B, the composition of f and g, which is denoted as fog(a)= f(g(a))....

Properties of Function Composition

fog ≠ gof f-1 of = f-1 (f(a)) = f-1(b) = a. fof-1 = f(f-1 (b)) = f(a) = b. If f and g both are one to one function, then fog is also one to one. If f and g both are onto function, then fog is also onto. If f and fog both are one to one function, then g is also one to one. If f and fog are onto, then it is not necessary that g is also onto. (fog)-1 = g-1 o f-1...

Applications in Engineering

Understanding injective, surjective, and bijective functions is crucial in various engineering disciplines:...

Conclusion – Classes of Functions

Injective, surjective, and bijective functions play a critical role in mathematics and engineering by providing a structured way to map and analyze relationships between sets. Understanding these classes of functions is essential for solving complex problems and designing efficient systems in various fields....

FAQs on Classes of Functions

What is an injective function?...