Show that the function f colon Z rightwards arrow Z defined by f left parenthesis x right parenthesis equals x squared plus x for all x element of Z is a many-one function.

Asked by abhinavsaini123 | 1st Jun, 2015, 09:35: PM

Expert Answer:

L e t space minus 1 comma space 0 element of space Z. W e space k n o w space t h a t space minus 1 not equal to space 0  f left parenthesis negative 1 right parenthesis space equals space left parenthesis negative 1 right parenthesis squared plus left parenthesis negative 1 right parenthesis space equals 1 minus 1 space equals space 0 space f left parenthesis 0 right parenthesis space equals space left parenthesis 0 right parenthesis squared plus left parenthesis 0 right parenthesis space equals 0 plus 0 space equals space 0  T h u s space minus 1 not equal to space 0 space b u t space space f left parenthesis negative 1 right parenthesis space equals f left parenthesis 0 right parenthesis.  S o comma space f space i s space a space m a n y minus o n e space f u n c t i o n.

Answered by Vijaykumar Wani | 2nd Jun, 2015, 11:47: AM

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