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Injective and Surjective Functions for IIT-JEE (Summary)
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This lesson explains the concept of one-one, many-one, onto and into functions. Also bijective functions have been explained in the last

Vineet Loomba is teaching live on Unacademy Plus

Vineet Loomba
IITian | No. 1 Educator in IIT-JEE (Maths) | 4 Million Minutes Watch Time | 8+ Years Experience | Youtube: Maths Wallah | vineetloomba.com

U
Unacademy user
G
sir theory part smaj me aa raha hai lekin question nahi ban rahe hai ,so sir gives question practice video lecture
sir bijective ko kase check kare ki bijective hai ki nahi koyi method hai kya
Vineet Loomba
2 months ago
Injective or surjective dono ch eck krke
sir bijective ko kase check kare ki bijective hai ki nahi koyi method hai kya
sir can u pls tell us that how to calculate no. of one-one or no. of onto function of a given function??
Vineet Loomba
2 months ago
Okay I will make a video
DA
sir iss topic pe bas ek question hi krwaya. Kuch aur jee ke ques. karwa dete !
Vineet Loomba
3 months ago
Krva dunga ..kisi ne maange nhi ques ..koi demand nhi thi
DA
Danish Alam
3 months ago
Okay. Thank you sir !
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  4. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) TYPES One-One Function (Injective Mapping) Many-One Function Onto Function (Surjective Mapping) Into Function Bijective mapping MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  5. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) (I) One-One Function (Injective): If each element in the domain of a function has a distinct image in the c then the function is said to be one-one function. o-domain f: A B is one-one at b f(a)=f(b)-> f(a)-f(b) for all a, be A a=b for all a, be A MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  6. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) (II Many-One Function: If there are two or more than two elements of domain aving the same image then f (x) is called Many-One function. X1 X2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  7. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) CHECKING INJECTIVITY Method I : if f(%) = f(X) Vx,x2 E D Method I HORIZONTAL LINE TEST: If any line parallel to x-axis cuts the graph of the function, atmost at one point, then the function is one-one. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  8. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Example MethodI f(x) = x2 + 3x + 2 f(x,)-f(x) It does not imply only x1 Let two points in domain are x, and x, x2 + 3x1 + 2 x22 + 3x2 + 2 Hence f (x) is many to one function. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  9. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Method II : Graph of y = x2 + 3x + 2 , line parallel to x-axis, cuts the curve more than one point hence it is many to one function. 2 MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  10. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Method II If domain of f(x) is continuous and dx > 0 If domain of f(x) is continuous and ax < 0, xin domain then f is One-One dy , V x in domain then f is One-One dy dy If dx takes both positive and negative signs, then the function is increasing as well as decreasing. So either we get a maximum value or a minimum value in the given domain. Hence function is many to one. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  11. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) Onto Function (Surjective Mapping) Let f : A B be a function. If each element in the co-domain B has at least one pre-image in the domain A ie. | Range of f = Co-domain | , then 'f' is called onto. Onto function are also called surjective MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)


  12. REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) (x) is both injective and surjective, then it is called a Bijective mapping The bijective functions are also named as invertible, non singular or biuniform functions. MATHEMATICS FOR IIT-JEE ER. VINEET LOOMBA (IIT RooRKEE)