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 .

Answer 1

Consider the function f,g:R→R defined as,

f( x )=x+1 g( x )=2x−3

(i)

( f+g )( x )=f( x )+g( x ) , for f,g:R→R

( f+g )( x )=( x+1 )+( 2x−3 ) =3x−2

(ii)

( f−g )( x )=f( x )−g( x ) for f,g:R→R

( f−g )( x )=f( x )−g( x ) =( x+1 )−( 2x−3 ) =x+1−2x+3 =−x+4

Thus, the value of ( f−g )( 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 2x−3 g( x )≠0 2x−3≠0 x≠ 3 2

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