Algebra of Real Function : Addition,Subtraction,Multiplication and Division

Algebra of Real Function

Real Value Function: A function which has all real number or subset of the real number as it domain Real Valued Function: A function which has all real number or subset of the real number as it range
For functions \(f:X - > {\bf{R}}\) and \(g:X - > {\bf{R}}\), we have

Addition \(\left( {f + g} \right)\left( x \right) = f\left( x \right) + g\left( x \right),x \in X\)

Substraction \(\left( {f - g} \right)\left( x \right) = f\left( x \right)-g\left( x \right),x \in X\)

Multiplication \(\left( {f.g} \right)\left( x \right) = f\left( x \right).g\left( x \right),x \in X\)

Multiplication by real number
\(\left( {kf} \right)\left( x \right) = kf\left( x \right),x \in X\), where \(k\) is a real number.

Division \(\frac{f}{g}\left( x \right) = \frac{{f(x)}}{{g(x)}}\)
\(x \in X\) and \(g\left( x \right) \ne 0\)