Answer
a)yes
b)No
c)No
d)yes
Work Step by Step
a) This function is onto, since every integer is 1 less than some integer. In particular, f(x + 1) = x.
b) This function is not onto. Since n^2 + 1 is always positive, the range cannot include any negative integers.
c) This function is not onto, since the integer 2, for example, is not in the range. In other words, 2 is not the
cube of any integer.
d) This function is onto. If we want to obtain the value x, then we simply need to start with 2x, since f(2x) = ⌈2x/2⌉ = ⌈x⌉ = x for all x ∈ Z.
