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

Function

A relation  f from  X to  Y is called ‘function’ if it satisfies the following conditions.

(i)  D_f =X

(ii)  (x,y) \in f and  (x,z) \in f \implies Y =Z

 \rightarrow If  f \subset X \times Y  is a function, then  f: X \rightarrow Y or X^f \rightarrow Y i.e.,  f is a function from  X to  Y or on  X to  Y or  f maps  X into   Y.

If  (x,y) \in f , then  y =f(x) , where   y is the value of   x or the image of x under  f .

 \rightarrow If f: X \rightarrow Y , then  y=f(x) , where every   x \in X, a unique element f(x) \in Y . The set   Y is called co-domain of  f .

 \rightarrow For any subset   A of  X , the image of  A under  f is the set

 f(A)= \{ f(x): x \in A\} and for any  B  \subseteq Y ,the pre-image of  B is the set

 f^{-1}(B)= \{x \in X: f(x) \in B\}

The range of  f is defined by R_f =f(x)= the set of all images of elements of  X under  f .

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