182k views
2 votes
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

User ARTLoe
by
8.5k points

1 Answer

4 votes

Final answer:

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.

User Pocockn
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories