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Suppose that g(x)=1+sqrt(x) " and " f(g(...

Suppose that `g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x.` Then find the function `f(x)`.

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`g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x " " `(1)
` :. f(1+sqrt(x))=3+2sqrt(x)+x`
Put `1+sqrt(x)=y " or " x=(x-y)^(2).` Then,
`f(y)=3+2(y-1)+(y-1)^(2)=2+y^(2).`
` :. f(x)=2+x^(2)`
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