**Category : **JEE Main & Advanced

(1) **Scalar multiplication of a function : \[(c\,f)(x)=c\,f(x),\]** where \[c\] is a scalar. The new function \[c\,f(x)\] has the domain \[{{X}_{f}}.\]

(2) **Addition/subtraction of functions **

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**\[(f\pm g)(x)=f(x)\pm g(x).\] **The new function has the domain \[X\].

(3) **Multiplication of functions **

\[(fg)(x)=(g\,f)(x)=f(x)g\,(x).\] The product function has the domain \[X\].

(4) **Division of functions :**

(i) \[\left( \frac{f}{g} \right)\,(x)=\frac{f(x)}{g(x)}.\] The new function has the domain \[X,\] except for the values of \[x\] for which \[g\,(x)=0.\]

(ii) \[\left( \frac{g}{f} \right)\,(x)=\frac{g(x)}{f(x)}.\] The new function has the domain \[X,\] except for the values of \[x\] for which \[f(x)=0.\]

(5) **Equal functions : **Two function \[f\] and \[g\] are said to be equal functions, if and only if

(i) Domain of \[f=\] Domain of \[g\]

(ii)** **Co-domain of \[f=\] Co-domain of \[g\]

(iii)** \[f(x)=g(x)\,\forall x\in \]** their common domain

(6) **Real valued function : **If \[R,\] be the set of real numbers and \[A,\,\,B\] are subsets of \[R,\] then the function \[f:A\to B\] is called a real function or real–valued function.

*play_arrow*Some Important Definitions*play_arrow*Intervals*play_arrow*Definition of Function*play_arrow*Domain, Co-domain and Range of Function*play_arrow*Algebra of Functions*play_arrow*Kinds of function*play_arrow*Even and Odd Function*play_arrow*Periodic Function*play_arrow*Composite Function*play_arrow*Inverse Function*play_arrow*Limit of a Function*play_arrow*Fundamental Theorems on Limits*play_arrow*Methods of Evaluation of Limits*play_arrow*Introduction*play_arrow*Continuity of a Function at a Point*play_arrow*Continuity From Left and Right*play_arrow*Discontinuous Function*play_arrow*Differentiability of a Function at a Point

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