. Show that the function f defined below from (0, 1] to (0, 1) is (i) well defined (i.e., s every member of the domain in the co-domain), (ii) injective and (iii) surjective. any x € (0, 1], f(x) = I n+1 if x for any n € Z+, for some ne Z+. n n

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Q7. Show that the function f defined below from (0, 1] to (0, 1) is (i) well defined (i.e.,
maps every member of the domain in the co-domain), (ii) injective and (iii) surjective.
For any x € (0, 1],
f(x) =
x if x for any n € Z+,
nif x=for some n € Z+.
Transcribed Image Text:Q7. Show that the function f defined below from (0, 1] to (0, 1) is (i) well defined (i.e., maps every member of the domain in the co-domain), (ii) injective and (iii) surjective. For any x € (0, 1], f(x) = x if x for any n € Z+, nif x=for some n € Z+.
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