# Math Help - Checking if a function is surjective

1. ## Checking if a function is surjective

I have this function

$y = (2x+1)/(x-1)$ where x is a real number not = 1

which i am trying to check if it is surjective.

I solve it:

$x = (y+1)/(y-2)$

Am I correct in saying that this is not surjective due to the fact that it does not have the restriction y not = 2 ?

Thank you

2. ## Re: Checking if a function is surjective

Originally Posted by iva
I have this function

$y = (2x+1)/(x-1)$ where x is a real number not = 1

which i am trying to check if it is surjective.

I solve it:

$x = (y+1)/(y-2)$

Am I correct in saying that this is not surjective due to the fact that it does not have the restriction y not = 2 ?

Thank you
The function is not surjective because there is no x such that y = 2.

3. ## Re: Checking if a function is surjective

the question depends on which range is specified......please defined function completely

4. ## Re: Checking if a function is surjective

Thanks, ok here is the full function (I was stuck at trying to determine the surjectivity and not really looking for an entire solution). Thanks for your reply alex but is this because due to the fact that y cannot be 2, and therefore the full spectrum of real numbers is not available as stated, is this why ut can't be surjective?

Here is the whole function (I struggled to try find big curly braces to go around everything):

$g:= R->R$

$g(x) = { (2x+1)/(x-1)$ if x not 1
$g(x) = { 2$ if x = 1

5. ## Re: Checking if a function is surjective

Originally Posted by iva
$g:= R->R$

$g(x) = { (2x+1)/(x-1)$ if x not 1
$g(x) = { 2$ if x = 1
This function is surjective.

6. ## Re: Checking if a function is surjective

Thanks, but what about the fact that that y cannot be 2 when you solve the first equation?

7. ## Re: Checking if a function is surjective

Originally Posted by iva
Thanks, but what about the fact that that y cannot be 2 when you solve the first equation?
Doesn't matter because the first equation by itself does not completely describe the function.

The important thing is that there is an x (namely 1) such that g(x) = 2.

8. ## Re: Checking if a function is surjective

I get it now! thanks so much