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Let f:R→R and g:R→R defined by f(x)=x 2...

Let `f:R→R and g:R→R defined by f(x)=x 2 and g(x)=(x+1)`. Show that `gof  =fog.`

Text Solution

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Given, `f(x)=x^{2}` and `g(x)=(x+1)`

`(g circ f)(x)=g{f(x)}=gleft(x^{2}right)=left(x^{2}+1right)`

`(f circ g)(x)=f{g(x)}=f(x+1)=(x+1)^{2}`

Hence, gof `equiv` fog.

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Knowledge Check

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