PAKMATH Knowledge Learning Point

In this post we define Inverse Hyperbolic Functions. The inverse hyperbolic Functions are expressed in terms of natural logarithms. FUNCTIONS FORMULAS Sinh-1 x   For all x Cosh-1 x Tanh-1 x Cosech-1 x Sech-1 x Coth-1 x  

In this post we define Hyperbolic  Functions and also discuss their domains and ranges. The  hyperbolic Functions have same properties that resembles to those of trigonometric functions. Functions                       Formulas y = Sinh x y = Cosh x  , Range=[1,+) y = Tanh x     y = Coseh x   y = Sech x    y = …

In this post we define Inverse Trigonometric Functions and also their domain and range. If you want to see their related topics then click here Function Range               and           Domain y = sin-1 x          y = cos-1 x           y = tan-1 x     

Trigonometric Functions We denote and define trigonometric functions as follows. Function Domain Range Y=Sinx R -1  ≤ Y ≤  1 Y=Cosx R -1 ≤  Y ≤  1 Y=Tanx {x: x ∈ R and x ≠(2n+1) } R Y=Cotx {x: x ∈ R and x ≠n } R Y=Secx {x: x∈ R and x≠(2n+1) } y ≥1,  y ≤  -1 Y=Cosecx …

   There are following Algebraic Functions.(1) Polynomial Function (2) Linear Function  (3) Identity Function  (4) Constant function  (5) Rational function   (1) Polynomial Function A function say P of the form P(x) = an xn+an-1 xn-1+an-2 xn-2+an-3 xn-3+. . . + a2 x2+ a1 x+a0 for all where the coefficient an, an-1,  an-2, . . . , a2, a1, a0 are real numbers and the exponents are non-negative integers, is called a polynomial …

  In this post, we define Solution of a Differential Equation, General Solutions,  Particular Solution, Equations with Separable Variables and also Linear Equations.   Solution of a Differential Equation   It is a  relation between variables not involving differential coefficients such that this relation and the derivatives obtained from it satisfy the given differential equation.   General Solutions:    A solution of a …

Function Domain and range of a function Inverse function Graph of Algebraic Function Algebraic Functions Trigonometric Functions Inverse Trigonometric Functions Hyperbolic Functions Inverse Hyperbolic Functions Explicit Function Implicit Functions Parametric function  

In this post we highlight the point that which graph is function and not a function.  If a vertical line intersects a graph in one point, it is the graph of a function. If a vertical line intersects a graph in more than one point, it is not the graph of a function.   READ MORE DEFINITIONS CLICK HERE

In this post we define inverse function and also provide an example to clear the concept of it. The inverse function of f denoted by f-1 is a function from Y onto X and is defined by x= f–1(y)  for all x in y if and only if as y=f(x) , for all x The set X of all possible input values is …

In this post, we find the domain and range of a function with the help of different examples. Example: 1 Find the domain and range  of x2. Solution.  Domain: Set of all real numbers Range:    Set of all non –negative real numbers. Example: 2 Find the domain and range  of    . Solution.  Domain: Set of all real numbers except -2 and …