Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Some different types of functions

(i) One-One (Injective):

If  f: A\rightarrow B is said to be one-one i.e.,  (x_1,y)\in f &  (x_2,y)\in f \implies x_1 = x_2

(ii) Onto (Surjective):

If  f: A\rightarrow B is said to be onto i.e.,  R_f = f(x)=y \implies \text { range } = \text {co-domain }.

(iii) One-one & Onto (Bijective):

If  f: A\rightarrow B is said to be bijective i.e.,  f is both injective & surjective i.e., one-one correspondence

(iv) Many-one:

A function  f: A\rightarrow B is said to be a many-one function, if two or more elements of  A have the same   f image in  B .

Thus  f: A\rightarrow B is many one if for  x_1,x_2 \in A,  f(x_1)=f(x_2) but  x_1\neq x_2.

(v) Into:

If  f: A\rightarrow B is into such that at least one element in codomain which is not the image of any element is domain.

Hence  Y_1 have no pre-image in  A .

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