injection/surjection/bijection questions

**p00ndawg** · October 17th 2009, 10:19 AM

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

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

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, $\infty$ )

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.

**Plato** · October 17th 2009, 10:39 AM

Originally Posted by p00ndawg

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

1. $F:$ $[3,\infty) \rightarrow [5, \infty)$ defined by $F(x) = (x-3)^2 {\color{red}-} 5$ .

Don't you mean $F(x)=(x-3)^2+5?$

For the other try
$\tan \left( {\frac{{\pi x}}<br /> {2}} \right)$

**p00ndawg** · October 17th 2009, 10:54 AM

Originally Posted by Plato

Don't you mean $F(x)=(x-3)^2+5?$

For the other try
$\tan \left( {\frac{{\pi x}}<br /> {2}} \right)$

ahh sorry it was x+3. fixed in op

$\tan \left( {\frac{{\pi x}}<br /> {2}} \right)$

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

**Plato** · October 17th 2009, 11:04 AM

Originally Posted by p00ndawg

$\tan \left( {\frac{{\pi x}}<br /> {2}} \right)$
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.

**p00ndawg** · October 17th 2009, 11:12 AM

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.

**Plato** · October 17th 2009, 11:58 AM

See

**p00ndawg** · October 17th 2009, 12:09 PM

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?

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