BUSINESS MATHEMATICS & STATISTICS
174
ALGEBRA OF FUNCTIONS By algebra of functions we mean the application of the four basic operations of addition, subtraction, multiplication, and division on any two or more functions. It is performed just in the same manner as it is done in case of simple arithmetic. Thus, if f(x) and g(x) are any two functions, then their four algebraic operations will be performed as under: (i) Addition of f(x) and g(x)=f(x)+g(x) (ii) Subtraction of g(x) from f(x)=f(x)-g(x) (iii) Multiplication of f(x) and g(x)=f(x).g(x)
(iv) Division of f(x) by
g (x) =
f (x) g (x)
The following illustration will show how algebra of functions are performed. Illustration Perform the four basic operations on the following two functions: Solution: (i) Addition:
f ( x ) + g ( x ) = ( 2x 2 − 5 ) + ( 3x + 5 )
= 2x 2 − 5 + 3x + 5 = 2x 2 + 3x (ii) Subtraction:
f ( x ) − g ( x ) = ( 2x 2 − 5 ) − ( 3x + 5 ) = 2x 2 − 5 − 3x − 5 = 2x 2 − 3x − 10
(iii) Multiplication:
f ( x ) .g ( x ) = ( 2x 2 − 5 ) . ( 3x + 5 ) = 6x 3 − 15x + 10x 2 − 25 = 6x 3 + 10x 2 − 15x − 25
2 f ( x ) ( 2x − 5 ) 2x 2 − 5 (iv) Division: = = g ( x ) ( 3x + 5 ) 3x + 5
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