Consider the function

\\\\int :Z->Z

given by\

f(m)={(m-7 if m is even ),(m+3 if m is odd ):}

\ (a) What kind of inputs will give you odd numbers as outputs?\ (b) What kind of inputs will give you even numbers as outputs?\ (c) What are all the integers

m

such that

f(m)=8

?\ (d) What are all the integers

m

such that

f(m)=3

?\ (e) Determine whether or not

\\\\int

is injective. Make sure you consider for each input.\ whether it is odd or even. Also, make sure to explain why it is either possible or\ impossible for

f(m)=\\\\int (n)

when

m

is odd and

n

is even.\ (I) Determine whether or not

f

is surjective. Make sure your solution considers both\ the case where your output is odd and the case where your output is even.

3. Consider the function :ZZ given by f(m)={m7m+3ifmisevenifmisodd (a) What kind of inputs will give you odd numbers as outputs? (b) What kind of inputs will give you even numbers as outputs? (c) What are all the integers m such that f(m)=8 ? (d) What are all the integers m such that (m)=3 ? (e) Determine whether or not is injective. Make sure you consider for each input whether it is odd or even. Also, make sure to explain why it is either possible or impossible for f(m)=f(n) when m is odd and n is even. (I) Determine whether or not f is surjective. Make sure your solution considers both the case where your output is odd and the case where your output is even