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Given examples of two functions `f:" "N ->N" "a n d""""""g:" "N->N` such that of is onto but f is not onto. (Hint: Consider `f(x)" "=" "x" "a n d""""""""g(x)" "=" "|x|` ) .

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`f(x) = x+ lxl + 1 ≥ 1 + 1 `
`=> f(x) ≥ 2`
Hence f is not onto
`gof (x) = g (f (x)) = g (x + 1) = (x+1) -1`
`=> gof (x) = x V x ∈ N `
∴ Range of gof = N as gof is the identity f
Hence gof is onto.
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