test for functions summary

The relation should be one-one or many-one, and Every first element is mapped which means that every pre-image should have an imag..

Every polynomial is continuous. Every rational function is continuou..

A function is a relation on A x B is which A function is a relation on A x B is which (i) no two second elements have a common first element. (ii) every first element has a corresponding second element. Every function is either one-one onto or one-one into or man..

Aldehydes, ketones, carboxylic acids and their functional derivatives (aryl halides, acid anhydrides, esters and amides) contain a carbonyl group and are highly polar molecule..

First Fundamental Theorem of Integral Calculus Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined ..

A group of individuals, having similar structural and functional characters, capable of potential interbreeding is termed as species. In nature all apecies exhibit cooperative and competitive interactions among the members of the species (intraspecific) and also with members of othe..

Let X be a set of numbers and f : N n --> X be a function, then the ordered set {f(1), f(2),...., f(n)} is called a finite sequence in X...

All living organisms are composed of one or more cells. A cell is the structural and functional unit of life. The metabolic reactions in a living organism - can occur only in a delicately balanced environment. Through their unique chemical composition, cells provide a specific ..

Growth is an irreversible increase in size and weight of an organism. The cells of the body do not grow uniformly but differentially. The main types of growth are auxetic, multiplicative and accretionary. The human growth curve is sigmoid and is controlled by hormones. Regeneration is of two types...

Polymers - high molecular mass macro-sized molecules consisting of repeating units of monomers - may be synthetic or natural in origin. Addition polymerization are usually performed on alkenes and their derivatives and proceed through chain growth mechanism involving radicals, cations and anio..