Question

definition of function?

Answer 1

a function[1] is a correspondence that associates each input with exactly one output. The output of a function f with input x is denoted f(x) (read "f of x"). For example, the rule f(x) = 2x defines a function f that associates any input number with the number twice as large. If x = 5 then f(x) = 10. Two different rules define the same function if they make the same associations, for example f(x) = 3x−x defines the same function as f(x) = 2x.

Answer 2

Formal description of a function typically involves the function's name, its domain, its codomain, and a rule of correspondence. Thus we frequently see a two-part notation, an example being

where the first part is read:
"ƒ is a function from N to R" (one often writes informally "Let ƒ: X → Y" to mean "Let ƒ be a function from X to Y"), or
"ƒ is a function on N into R", or
"ƒ is an R-valued function of an N-valued variable",
and the second part is read:
maps to
Here the function named "ƒ" has the natural numbers as domain, the real numbers as codomain, and maps n to itself divided by π. Less formally, this long form might be abbreviated

where f(n) is read as "f as function of n" or "f of n". There is some loss of information: we no longer are explicitly given the domain N and codomain R.
It is common to omit the parentheses around the argument when there is little chance of confusion, thus: sin x; this is known as prefix notation. Writing the function after its argument, as in x ƒ , is known as postfix notation; for example, the factorial function is customarily written n!, even though its generalization, the gamma function, is written Γ(n). Parentheses are still used to resolve ambiguities and denote precedence, though in some formal settings the consistent use of either prefix or postfix notation eliminates the need for any parentheses.
To define a function, sometimes a dot notation is used in order to emphasize the functional nature of an expression without assigning a special symbol to the variable. For instance, stands for the function , stands for the integral function , and so on...

Answer 3

hai vishal i want simple definition.

Answer 4

u in which grade?

Answer 5

b.sc., level.

Answer 6

A function, denote it by f, from a set A to a set B is a relation from A to B that satisfies
for each element a in A, there is an element b in B such that <a, b> is in the relation, and
if <a, b> and <a, c> are in the relation, then b = c ...

Answer 7

it is of school level only as i am also in school...