I'll try to give some hints rather than the functions themselves.

a) Map even positive integers into positive integers and odd positive integers in to negative integers. Don't forget to map one number to 0.

b)Stretchthe interval. What do multiply by? Notice that a(x- 1)+ 1 will map 1 to 1 no matter what a is.

c)Stretchagain! Only now you have to find a way to map 0 to negative infinity and 1 to positive infinity.

(d) A little bit tricky. Map the irrationals to themselves. The remaining rational numbers in (0, 1) can be put into a list: , , etc. Map the first rational, , to 0, the second, , to 1 and I'll let you decide what to do with the rest of them.