Not an urgent question just curious.
***
I know I could graph this and find the range easily, (In fact, I already have) but I want to know if I can find the range from just the equation below:

Question

Not an urgent question just curious.
***
I know I could graph this and find the range easily, (In fact, I already have) but I want to know if I can find the range from just the equation below:

cecil_the_weasel · Answer

$$f(x)= \frac{ 2x+5 }{ 4x+7}$$

I know how to do this with quadratic equations but I can't remember if there is a way to do it with a problem like this. Thanks :D

johnweldon1993 · Answer

Well remember that the range is the same as the domain of the inverse function

So find $\large f^{-1}(x)$ and find the domain and you will have your range :)

thesmartone · Answer

John has suggested the only really nice way to do it. 

There is no easy way to find range besides looking at a graph. Finding the domain is easier. It's usually always all real numbers except when a value of x makes the denominator 0 or it makes a square root negative. 

And so if you find the domain of the inverse function, that's the same as finding the range of the function. :)

cecil_the_weasel · Answer

Thanks both of you :)
This helped a lot.

thesmartone · Answer

Thank John, haha. This question came up in class the first day of Calc 1 and the TA had no proper response and John just gave me the solution to it and it's a "Why didn't I think of this before?" moment, haha. xD