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Question

Let f , g : R → R be defined, respectively by f ( x ) = x + 1, g ( x ) = 2 x – 3. Find f + g , f – g and .

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Solution

Consider the function f,g:RR defined as,

f( x )=x+1 g( x )=2x3

(i)

( f+g )( x )=f( x )+g( x ) , for f,g:RR

( f+g )( x )=( x+1 )+( 2x3 ) =3x2

(ii)

( fg )( x )=f( x )g( x ) for f,g:RR

( fg )( x )=f( x )g( x ) =( x+1 )( 2x3 ) =x+12x+3 =x+4

Thus, the value of ( fg )( x ) is x+4 .

(iii)

( f g )( x )= f( x ) g( x ) , where g( x ) is not equal to zero.

( f g )( x )= x+1 2x3 g( x )0 2x30 x 3 2

Thus, the value of ( f g )( x ) is x+1 2x3 ,x 3 2 .


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