मान लीजिएः `f: R to R`, जहाँ `f(x)=2x+1, g:R to R`, जहाँ `g(x)=x^(2)-2` तो
(i) (gof)(x) (1) का मान बताइएः
सिद्ध कीजिएः की `(gof) ne (fog)`.

Explanation

`" "(gof)(x)=g[f(x)] `
`" "=g[2x+1]" "[therefore f(x)=2x+1]`
`" "=(2x+1)^(2)-2`
`" "=4x^(2)+1+4x-2`
`" "=4x^(2)+4x-1`
(gof)(1)=`4(1)^(2)+4(1)-1`
`" "=4+4-1`
`" "=7`
(ii) `(gof)(x)=4x^(2)+4x-1`
and (fog)(x)=f[g(x)]
=`f[x^(2)-2]" "[therefore g(x)=x^(2)-2]`
`" "=2(x^(2)-2)+1`
`" "=2x^(2)-3`
अंत: स्पस्ट
`(gof) ne (fog)`