Let 'A' and 'B' be any two non–empty sets, then a function '' from 'A' to 'B' is called Constant Function if and only if range of '' is a singleton.
Let be a function then a function '' from 'A' to 'B' is called a constant function if , whose is a constant.
The function defined by algebraic expression are called algebraic function.
A function of the form
Where 'n' is a positive integer and are real number is called a polynomial function of degree 'n'.
A polynomial function with degree '' is called a linear function. The most general form of linear function is
A polynomial function with degree '2' is called a Quadratic function.
The most general form of Quadratic equation is
A polynomial function with degree '3' is called cubic function.
The most general form of cubic function is
Let be a function then '' is called on identity function. If .
A function defined by , where both andare polynomial function is called, rational function.
A function, etc, then is called trigonometric function.
A function in which the variable appears as exponent (power) is called an exponential function
e.g. (i) (ii) .
A function in which the variable appears as an argument of logarithmic is called logarithmic function.
The following are hyperbolic functions:
Inverse Hyperbolic Functions:
The following are inverse hyperbolic functions:
When the dependent function is expressed clearly in terms of the independent variables, the function is said to be explicit function.
An implicit function is that which contains two or more variables that are not independent of each other.
A function in which 'x' and 'y' are expressed as functions of 3rd variables is called a parametric function.
In term of same variables.
Show that the parametric equations and represent the equation.
Squaring and adding (1) and (2)
A function is said to be an even function, if
Replace 'x' by ''
It is an even function.
A function is said to be an odd function if
Replace 'x' by ''
It is an odd function.