Real Function
A real valued function f : A to B or simply a real function 'f ' is a rule which associates to each possible real number x A, a unique real number f(x) B, when A and B are subsets of R, the set of real numbers. In other words, functions whose domain and co-domain are ..
A real valued function f : A to B or simply a real function 'f ' is a rule which associates to each possible real number x A, a unique real number f(x) B, when A and B are subsets of R, the set of real numbers. In other words, functions whose domain and co-domain are ..4. Into function
There is at least one element of B which has no pre-image. In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into. For types of functions, the four arrow diagrams given for one-one and many-one are repeated for ONT..
There is at least one element of B which has no pre-image. In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into. For types of functions, the four arrow diagrams given for one-one and many-one are repeated for ONT..Boolean Functions
An expression consisting of combinations of binary operations +, . and unary operation and a finite number of elements of a Boolean algebra is called a Boolean function..
Hyperbolic Function
We define (e x +e - x )/2 as sinhx and (e x -e -x )/2 as coshx. Based on this other trigonometric functions are defined and they are all called hyperbolic functions..
Function Summary
Summary - 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..
3. Onto function
Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..
Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..Identity function
A function f : R R is said to be an identity function if for all x R, f(x) = x. Domain = R Range = ..
A function f : R R is said to be an identity function if for all x R, f(x) = x. Domain = R Range = ..Representation of a Function
A function can be represented by the following methods: (i) An arrow diagram. (ii) Cartesian graph. (iii) Set-builder notatio..
Polynomial function
A function f : R R is said to be a polynomial function if for each x R, f(x) is a polynomial in x. f(x) = x 3 + x 2 + x ..
A function f : R R is said to be a polynomial function if for each x R, f(x) is a polynomial in x. f(x) = x 3 + x 2 + x ..Area function
We have already defined, for a continuous function f(x) on a closed interval [a, b] as the area of the region bounded by the curve y = f(x), X-axis and x= a and x = b. In other words, area of the shaded region is a function of x. The function A(x) is shown in figure be..
We have already defined, for a continuous function f(x) on a closed interval [a, b] as the area of the region bounded by the curve y = f(x), X-axis and x= a and x = b. In other words, area of the shaded region is a function of x. The function A(x) is shown in figure be..See what our Users say :
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