1. ## injection/surjection/bijection questions

Classify each function as injective, surjective, bijective, or none of these.

1. $\displaystyle F:$ $\displaystyle [3,\infty) \rightarrow [5, \infty)$ defined by $\displaystyle F(x) = (x+3)^2 - 5$

Show that the following pairs of sets S and T are equinumerous by finding a specific bijection between the sets in each pair.

(d) S = (0,1) and T = (0,$\displaystyle \infty$)

I dont understand how to d really at all. I know with easier points we were just finding the line from the two points, but im not quite sure how to deal with harder or bigger points.

2. Originally Posted by p00ndawg
Classify each function as injective, surjective, bijective, or none of these.

1. $\displaystyle F:$ $\displaystyle [3,\infty) \rightarrow [5, \infty)$ defined by $\displaystyle F(x) = (x-3)^2 {\color{red}-} 5$.
Don't you mean $\displaystyle F(x)=(x-3)^2+5?$

For the other try
$\displaystyle \tan \left( {\frac{{\pi x}} {2}} \right)$

3. Originally Posted by Plato
Don't you mean $\displaystyle F(x)=(x-3)^2+5?$

For the other try
$\displaystyle \tan \left( {\frac{{\pi x}} {2}} \right)$

ahh sorry it was x+3. fixed in op

$\displaystyle \tan \left( {\frac{{\pi x}} {2}} \right)$

how did you come up with that? Are you just guessing what fits in that domain and range?

4. Originally Posted by p00ndawg
$\displaystyle \tan \left( {\frac{{\pi x}} {2}} \right)$
how did you come up with that? Are you just guessing what fits in that domain and range?
It is hardly a guess! I have taught this so long I know most of the tricks.
But in any case, graph the functions in both problems.
The answers will jump out at you.

5. Originally Posted by Plato
It is hardly a guess! I have taught this so long I know most of the tricks.
But in any case, graph the functions in both problems.
The answers will jump out at you.

haha yea i know you're not guessing, but I was speaking like for me in order to find a specific function that fills the gap I would probably just have to guess something right?

after graphing them I saw the first one clearly.

But for the second I graphed it and just see what almost looks like a straight line across the x axis. Im not sure what thats telling me.

6. See

7. Originally Posted by Plato
See

ahh you're right, well of course you were right, i had my calculator in degrees.

Thank you.

So if my teacher gives me a problem similar to this on a test, is there any kind of strategy involved in figuring out what function meets the requirements?