## Vineet Loomba is teaching live on Unacademy Plus

IIT-JEE CRASH COURSE FOR SURE SHOT SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Search vineet loomba unacademy" on GOOGLE IIT-JEE MATHS REVISION COURSE PREPARED BY: ER. VINEET LOOMBA IITian | IIT-JEE MENtOR

REVISION COURSE FOR JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. Doubts/Feedback in Comment Section. Comment other topics you want to revise. Follow me @ https://unacademy.com/user/vineetloomba to get updates. Share among your peers as SHARING is CARING !!

SETS, RELATIONS, FUNCTIONS #INJECTIVE SURJECTIVE FUNCTIONS IIT-JEE MATHS REVISION COURSE PREPARED BY: ER. VINEET LOOMBA IITiAN | IIT-JEE MENTOR FoR SURE SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE)

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)

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)

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)

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)

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)

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)

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)

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)

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)