Let `Y = {n^2: n in N} in N`. Consider `f : N ->Y`as `f(n)=n^2`. Show that f is invertible. Find the inverse of f.

Explanation

`Y={n^{2}: n in N}`
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f: N arrow Y` here `f(n)=n^{2}`
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g: Y arrow N,` defined by `g(y)=sqrt{Y}`
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(gof)(n)=g(n)=g(n^{2})=sqrt{n^{2}}=n`
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(fog)(y)=f(g(y))=f(sqrt{y}=(sqrt{y})^{2}=y. `
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therefore god=1_{N} and {fog}=1_{y}}`
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therefore f` is invertible with `f^{-1}=g.`
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