Question

Which of the following are functions from z to z?

1) f(x) = x²
2) g(x) = |x|
3) h(x) = x + 1
4) k(x) = 1/x

Answer 1

Functions f(x) = x², g(x) = |x|, and h(x) = x + 1 map integers to integers, and thus are functions from z to z, while k(x) = 1/x is not because division by an integer does not always result in an integer.

Step-by-step explanation:

The question 'Which of the following are functions from z to z?' asks us to determine which given expressions can be considered functions that map integers to integers. Here are the analyses for each option:

• f(x) = x² is a function from z to z because squaring any integer will result in another integer.
• g(x) = |x| is also a function from z to z because the absolute value of any integer is an integer.
• h(x) = x + 1 is a function from z to z because adding 1 to any integer results in another integer.
• k(x) = 1/x is not a function from z to z because the division of 1 by an integer does not always result in an integer, e.g., 1/2 is not an integer.

Therefore, functions f(x), g(x), and h(x) are functions from z to z, while k(x) is not.