For each of the following functions, give whether it is an injection or not, and whether it is a surjection or not, and fully justify your answer. (If it is an injection, prove it by showing that for any elements x is not equal to y, f(x) is not equal to f(y); if it isnt an injection, give an example of two inputs in the domain that produce the same output.

If it is a surjection, prove it by showing that for any element y in the target set, there is an element x in the domain such that f(x) = y; if it isnt, give an example of an element of the target set that no input can produce.)

a. f : NN; f(x) = 2x

b. g : RR; g(x) = 2x

c. h : NQ; h(x) = x 4

d. j : RR; j(x) = x3 + 2.