Relations and Functions II

Videos

Variety adds flavour 1

315

Variety adds flavour 2

68

What goes in determines what comes out 1

335

What goes in determines what comes out 2

167

Time for a quick test

86

The family of functions 1

204

The family of functions 2

84

Relations of main importance 1

143

Relations of main importance 2

239

Domain and range are tricky customers 1

131

Domain and range are tricky customers 2

89

Inverse is also a function 1

179

Inverse is also a function 2

136

Introduction to Relations

873

Domain, Range and Codomain of Relation

231

Void, Universal and Identity Relation

565

Reflexive, Symmetric and Transitive Relation

986

Equivalence Relation

1206

Number of Reflexive, Symmetric and Equivalence Relations

1081

Operations on Equivalence Relations

1481

Inverse Relation

522

Function as a Special Relation

744

Domain, Codomain and Range of Function

730

Algebra of Real Functions

998

Implicit and Explicit Functions

495

Bounded and Homogeneous Function

745

Even and Odd Functions

1015

Properties of Even and Odd Functions

2878

One-One/Many One Function

480

Graphical Method to Check One-one/Many-one

752

Algebraic Method to Check One-one/Many-one

784

Calculus Method to Check One-one/Many-one

1149

Onto Functions and Into Functions

597

Bijective Functions

536

Number of Different Types of Functions - I

706

Number of Different Types of Functions - II

2344

Introduction to Composite Functions

774

Composition of Non-uniformly Defined Functions

1370

Domain and Range of Composite Functions

1447

Properties of Composite Functions

3833

Definition of Inverse Function

590

Steps to Find Inverse Function

2872

Properties of Inverse Functions

460

Inverse of Composite Functions

1272

Graph of Inverse Function

571

Introduction to Periodic Functions

559

Properties of Periodic Functions

1640

Period of Combination of Two Functions

2354

Periods of Trigonometric Functions

1203

Composition of Periodic Function

1692

Functional Equations

4700

Introduction to Binary Operations

983

Types of Binary Operations

999

Distributive Binary operation

612

Identity Element

623

Inverse of an element

748

Introduction to Relations

383

Set Builder Form of a Relation

144

Ways of Represenation of Relations

164

Domain, Range and Codomain of a Relation

351

Number of Relations

61

Void Relation and Universal Relation

326

Identity Relation

139

Reflexive Relation

134

Symmetric Relation - I

185

Symmetric Relation - II

132

Transitive Relation

183

Property of Identity Relation

336

Equivalence Relation

198

Number of Reflexive Relations

259

Number of Symmetric Relations

321

Number of Equivalence Relations

439

Intersection & Union of 2 Equivalence Relations

409

Equivalence Class

394

Properties of Equivalence Classes

259

Inverse Relation

312

Properties of Inverse Relation

208

Function as a Special Relation

270

Not All Relations are Functions

243

Total Number of Functions from One Set to the Other Set

214

Image and Pre-image

175

Domain, Codomain and Range of a Function

284

Domain and Range of a Graph

134

Real Valued Function

327

116

Equal Functions

68

Addition and Subtraction of Functions

213

Multiplication of Two Functions

152

Division of Two Real Functions

121

Implicit and Explicit Functions

247

Bounded Functions

379

Homogeneous Functions

156

434

368

Properties of Even and Odd Functions - I

218

Properties of Even and Odd Functions - II

312

Sum or Difference

409

Product or Divison - I

507

Product or Divison - II

93

304

265

One-One Functions

285

Many-One Functions

191

Graphical Method to Check - I

580

Graphical Method to Check - II

99

Algebraic Method to Check

396

Calculus Method to Check

569

252

346

Combinations of One-one, Many-one, Onto & Into

285

Bijective Functions

235

Number of Total Functions

221

Number of One-one & Many-one Functions

488

Inclusion/Exclusion Principle - I

181

Inclusion/Exclusion Principle - II

15

Number of Onto & Into Functions - I

438

Number of Onto & Into Functions - II

364

Number of Constant & Bijective Functions - I

277

Number of Constant & Bijective Functions - II

140

Composite Functions - I

642

Composition of Uniformly Defined Function

128

Composition of Non-Uniformly Defined Function

282

Composition of Three or More Functions

279

Domain of Composite Functions

301

Non-commutative Nature

438

Associative Nature - I

175

Associative Nature - II

329

Composition of One-one Functions

357

Composition of Onto Functions

201

Composite Function is One-one

399

Composite Function is Onto

383

Composition of Even & Odd Functions

644

Introduction to Inverse Functions

268

Conditions for Inverse Function

322

Definition of Inverse Function - I

329

Definition of Inverse Function - II

154

Invertibility of Given Function - II

147

Algebraic Method to Find Inverse - I

141

Algebraic Method to Find Inverse - II

243

Inverse Functions are Bijective

301

Inverse of Composite Functions

352

Inverse of Inverse Function

439

Graph of Inverse Function

302

Intesection Points of Graph of Inverse Function

252

Introduction to Periodic Functions

400

Playing with Periodic Functions.

319

Operations on Periodic Function - I

385

Operations on Periodic Function - II

334

Periods of Trigonometric Functions

468

Sum of Periodic Functions

463

Periodicity of Combinations of Functions - I

325

Periodicity of Combinations of Functions - II

155

Period of Combinations of Functions

200

Powers of Trigonometric Functions - I

431

Powers of Trigonometric Functions - II

231

Periodicity of Composite Functions - I

98

Periodicity of Composite Functions - II

300

Periodicity of Constant Functions - I

318

Periodicity of Constant Functions - II

99

Practice: Periodic Functions - I

81

Practice: Periodic Functions - II

121

Introduction to Functional Equations

366

Some Functional Equations - 1

133

Some Functional Equations - 2

118

Some Functional Equations - 3

103

Some Functional Equations - 4

348

Some Functional Equations - 5

150

Minimum and Maximum Function

297

Introduction to Binary Operations

402

Binary Operations Table

479

Associative Binary operation

216

Distributive Binary operation - I

329

Distributive Binary operation - II

25

Identity Element

365

Inverse of an Element

323

Theorems on Inverse of an Element - I

139

Theorems on Inverse of an Element - II

130

Basics Of Relations

1105

Types Of Relations - I

1552

Types Of Relations - II

1206

More On Relations

2562

Inverse Relation

522

Introduction To Functions

3148

Classification Of Function - I

1240

Classification Of Function - II

1015

Properties Of Even & Odd Functions

2878

One-One/Many-One Functions - I

1232

One-One/Many-One Functions - II

1934

Onto & Into Functions

597

Bijective Function

536

Number Of Functions - I

706

Number Of Functions - II

2344

Composite Functions

774

Properties Of Composite Functions

6650

Inverse Function

590

Steps To Find Inverse Function

2872

Properties Of Inverse Functions - I

460

Properties Of Inverse Functions - II

1272

Properties Of Inverse Functions - III

571

Periodic Function

559

Properties Of Periodic Functions - I

3994

Invertibility of Given Function - I

211

Composite Functions - II

178

Substitution Method to Find Solutions

189

Commutative Binary operation

391

Basics of Relations

1105

Types of Relations - I

1552

Types of Relations - II

1206

More on Relations

2562

Inverse Relation

522

Introduction to Functions

3148

Classification of Function - I

1240

Classification of Function - II

1015

Properties of Even & Odd Functions

2878

One-One/Many-One Functions - I

1232

One-One/Many-One Functions - II

1934

Onto & Into Functions

597

Bijective Function

536

Number of Functions - I

716

Number of Functions - II

2344

Composite Functions

774

Properties of Composite Functions

6650

Inverse Function

590

Steps to Find Inverse Function

2872

Properties of Inverse Functions - I

453

Properties of Inverse Functions - II

1269

Properties of Inverse Functions - III

571

Periodic Function

559

Properties of Periodic Functions - I

3994

Properties of Periodic Functions - II

1204

Properties of Periodic Functions - III

1693

Special Functional Equations

4700

Binary Operations

983

Types of Binary Operations - I

999

Types of Binary Operations - II

613

Identity Element & Inverse Element

1372

222

202

90

177

66

308

305

168

115

84

213

226

53

138

207

197

242

120

91

84

133

59

181

125

72

84

118

500

171

118

197

282

150

258

510

258

206

187

111

221

328

183

275

80

281

369

394

45

93

204

46

117

293

235

394

144

277

259

114

282

563

89

142

162

217

123

126

124

167

160

178

379

426

491

361

410

28

114

133

128

100

43

115

81

56

118

219

115

305

138

207

118

118

111

221

328

369

293

114

219

282

563

160

178

379

426

491

222

202

90

56

177

66

308

305

168

115

84

213

226

53

138

207

197

242

120

91

84

133

115

59

181

125

72

84

118

118

500

171

118

197

282

150

258

510

258

206

187

111

221

328

183

275

80

281

369

394

45

93

204

46

117

293

235

394

277

259

114

219

282

563

89

142

162

217

123

126

124

167

160

178

379

426

491

361

410

28

114

133

128

100

43

115

81

144