Let 𝑓: ℕ ⟶ ℕ by defined by 𝑓(𝑥) - 2𝑥 for all 𝑥 ∈ ℕ where ℕ is the set of natural numbers. Showthat 𝑓 is one - one but not onto function.

Question

Let 𝑓: ℕ ⟶ ℕ by defined by 𝑓(𝑥) - 2𝑥 for all 𝑥 ∈ ℕ where ℕ is the set of natural numbers. Showthat 𝑓 is one - one but not onto function.
🧐 Not the exact question you are looking for?Go ask a question

Solution 1

Sure, let's break this down:

  1. One-to-One (Injective) Function: A function is said to be one-to-one (or injective), if the pre-image of every element in the range is unique. In other words, if different elements in the domain have different images in the co-domain.

    To prove that 𝑓 is one-t Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study pro

t Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to sol

This problem has been solved

Similar Questions

Let 𝑓: ℕ ⟶ ℕ by defined by 𝑓(𝑥) - 2𝑥 for all 𝑥 ∈ ℕ where ℕ is the set of natural numbers. Showthat 𝑓 is one - one but not onto function.

The function 𝑓f is defined by 𝑓(𝑥)=2𝑥+147f(x)= 72x+14​ , and 𝑓(𝑎)=6f(a)=6, where 𝑎a is a constant. What is the value of 𝑎a?

The piecewise-function 𝑓(𝑥) has opposite expressions. 𝑓(𝑥)={2𝑥−1,𝑥<00,𝑥=0−2𝑥+1,𝑥>0Which is the graph of 𝑓(𝑥)

Let f be a function such that 𝑓(−𝑥) = −𝑓(𝑥)  for all x. If ∫02𝑓(𝑥)𝑑𝑥=5, then ∫−22(𝑓(𝑥)+6)𝑑𝑥=Responses661616242434

Let R be a relation on the set N of natural numbers defined by nRm Û n is a factor of m (i.e., n|m). Then R is

1/3