Functions Formula for 12th Class

1. Definition of function :

Definition of function

2. Domain , Co – Domain and Range of a Function :

Domain , Co - Domain and Range of a Function

3. Formula for the Domain of a function.

Formula for the Domain of a function

4. Working Rule to find the Domain and Range of a Function.

Working Rule to find the Domain and Range of a Function

Example :

Working Rule to find the Domain and Range of a Function

5. Types of Function:

5.1  Mapping of Function :

(i). One – One function (Injective function) :

One - One function (Injective function)

(ii). Many – One function :

Many - One function

(iii). Into function :

Into function

(iv). Onto – function ( Surjective Function ) :

Onto - function ( Surjective Function )

5.2 Algebraic Functions : – These are the functions consisting of finite number of terms involving power and radicals of the independent variable , constants and fundamental mathematical operations (+) , (-) , (÷) (×)

(i). Polynomial Functions :

Polynomial Functions

(ii). Fractional Rational Functions :

Fractional Rational Functions

(iii). Irrational Function :

Irrational Function

5.3 Transcendental Function : The functions which are not algebraic are called transcendental function.

(i). Exponential

(ii). Logarithmic

(iii). Trigonometric

(iv). Inverse trigonometric functions are transcendental functions.

(i). Exponential Function :

Exponential Function

Case (a) : –

Exponential Function

Case (b) :

Exponential Function

(ii). Logarithmic Function :

Logarithmic Function

Note :

Logarithmic Function

Properties of logarithmic Function :

Properties of logarithmic Function

(iii). Trigonometric Function :

(a). Sine Function : – F(x) = Sinx

Sine Function

(b). Cosine Function : F(x) = Cosx

Cosine Function

(c). Tangent Function : F(x) = Tanx

Tangent Function

(d). Cosecant Function : f(x) = Cosecx is periodic with period 2π.

Cosecant Function

(e). Secant Function : f(x) = Secx is periodic with period 2π.

Secant Function

(f). Cotangent Function : F(x) = Cotx is periodic with period π.

Cotangent Function

(iv). Inverse Trigonometric Curves : 

Inverse Trigonometric Curves

Inverse Trigonometric Curves

Inverse Trigonometric Curves

5.4 Piecewise Function : As discussed piscussed picewise function are :

(i). Absolute value function (or modulus Function )

(ii). Signum Function

(iii). Greatest interger function

(iv). Fractional part function

(v). Least interger function.

(i). Absolute value function (or modulus Function ) : 

Absolute value function (or modulus Function )

Properties of modulus function.

Properties of modulus function

(ii). Signum Function : y = Sgn(x) 

Signum Function

(iii). Greatest interger function : 

Greatest interger function

Properties of greatest integer function :

Properties of greatest integer function

(iv). Fractional part function : 

Fractional part function

Properties of fractional part of x.

Properties of fractional part of x

(v). Least interger function : 

Least interger function

Properties of fractional part of x.

Properties of fractional part of x

5.5 Constant function : 

Constant function

5.6 Principal square root function : 

Principal square root function

5.7 Equal or Identical Function : 

Equal or Identical Function

5.8 Odd Function :

Odd Function

5.9  Even Function :

Even Function

5.10 Geometrical Curves :

(i). Straight line :

Straight line

(ii). Quadratic Equations :

Quadratic Equations

(iii). Circle :

Circle

(iv). Parabola :

Parabola

(v). Hyperbola :

Hyperbola

(vi). Ellipse : 

Ellipse

5.11 Monotonic Function :

(i). Increasing Function : Strictly increasing and Non decreasing function.

Strictly increasing function

(b). Decreasing Function : Strictly decreasing and Non increasing Function.

Decreasing Function

5.12 Periodic Function : 

Periodic Function

5.13 Composite Function : 

Composite Function

Properties of Composite Function :

Properties of Composite Function

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