Finding the image of a function

I've read the definition and examples of domain, co-domain and images, and understand the the image is the end result of the relationship between the domain and codomain. But, why then is it always expressed in terms of x when x is commonly used in the domain, or am i missing something. As an example i had to find the image of the function

$\displaystyle f(x) = 5/(2+x^2)$

and if I follow the same steps as other examples I get the result

image f = {x|x element of R and 0 < x =< 5/2}

seeing as

$\displaystyle (2+x^2) >= 2$

Is this right though?

Thank you

Re: Finding the image of a function

Quote:

Originally Posted by

**iva**

$\displaystyle f(x) = 5/(2+x^2)$

**image** f = {x|x element of R and 0 < x =< 5/2}

seeing as

$\displaystyle (2+x^2) >= 2$

Is this right though?

That is correct.