3. Prove thatf: N: N → N, defined by/ (m) m m2 + m + 1 for all m e N

1.	3. Prove thatf: N: N → N, defined by/ (m) m m2 + m + 1 for all m e N, is oneOne but not onto.
Answer» how it is not onto see if onto na as function is from N to N so let ki 2 be image what i have solved above na tells that 2 will be image but for that you have to put (-1+ or - sqrt5)/2 in place of m but function ka domain is from N and (-1+ or - sqrt5)/2 is irrational value so not possible.

3. Prove thatf: N: N → N, defined by/ (m) m m2 + m + 1 for all m e N, is oneOne but not onto.

Answer»

how it is not onto

see if onto na as function is from N to N so let ki 2 be image what i have solved above na tells that 2 will be image but for that you have to put (-1+ or - sqrt5)/2 in place of m but function ka domain is from N and (-1+ or - sqrt5)/2 is irrational value so not possible.

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3. Prove thatf: N: N → N, defined by/ (m) m m2 + m + 1 for all m e N, is oneOne but not onto.

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