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If phi(x)=lim(nrarrinfty)(x^(2n)f(x)+g(x...

If `phi(x)=lim_(nrarrinfty)(x^(2n)f(x)+g(x))/(1+x^(2n))`, then

A

`phi(x)=g(x)` for all `x in R`

B

`phi(x)=f(x)` for `x in R`

C

`phi(x)={(g(x),"for -1"ltxlt1),(f(x),"for|x|"ge1):}`

D

`phi(x)={(g(x),"for|x|"lt1),(f(x),"for|x|"gt1),((f(x)+g(x))/2,"for |x|"=1):}`

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The correct Answer is:
D
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