AlexMaths: Class 10

A relation f between two non-empty sets A and B is called a function from A to B if, for each a ∈ A there exists only one b ∈B such that (a,b) ∈ f .That is, f ={(a,b)| for all a ∈ B, b∈B }. A function is also called as a mapping or transformation

A function is also called as a mapping or transformation
The set A is called the domain of the function f and the set B is called its co-domain.
If f (a) = b, then b is called ‘image’ of a under f and a is called a ‘pre-image’ of b.
The set of all images of the elements of A under f is called the ‘range’ of f.
Every function is a relation. Thus, functions are subsets of relationsand relations are subsets of cartesian product
The range of a function is a subset of its co-domain.

Example

Let X = {1,2, 3, 4} and Y = {2, 4,6, 8,10} and R = {(1,2),(2,4),(3,6),(4,8)}.

Show that R is a function and find its domain, co-domain and range?

Solution: From the diagram, we see that for each x∈ X , there exists only one y ∈Y .

Thus all elements in X have only one image in Y. Therefore R is a function.

Domain X = {1,2,3,4}; Co-domain Y = {2,3,6,8,10}; Range of f = {2,4,6,8}.

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Class 10 Science Unit 2 Optics

Introduction

Properties of light

Refraction of light

Refraction of composite Light - Dispersion of Light

Scattering of light

Lens Types and Image formation Rules

Image Formation and Applications of Convex Lens

Image Formation and Applications of Concave Lens

Lens Formula magnification Lens Makers formula power of Lens

Human Eye Structure and Working

Defects in Eye