Please Login to access more options.

Problem 43: (Practice With Injective And Surjective)

For each function below, state the domain and codomain, determine if the function is injective, and then determine if the function is surjective.

  1. Let $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=x^2$.
  2. Let $f:[0,\infty)\to\mathbb{R}$ be defined by $f(x)=x^2$.
  3. Let $f:\mathbb{R}\to [0,\infty)$ be defined by $f(x)=x^2$.
  4. Let $f:[0,\infty)\to[0,\infty)$ be defined by $f(x)=x^2$.

As always, remember to justify each claim you make.

The following pages link to this page.

Here are the old pages.