1. ## Range

Does anyone know a good way of finding the range of a function...I usually either man it out and look for the wholes and check its horizontal endpoints...or if its a simple function I find its inverse and check that functions domain

2. Originally Posted by Mathstud28
Does anyone know a good way of finding the range of a function...I usually either man it out and look for the wholes and check its horizontal endpoints...or if its a simple function I find its inverse and check that functions domain
One word: Graph it.

3. Originally Posted by Mathstud28
Does anyone know a good way of finding the range of a function...I usually either man it out and look for the wholes and check its horizontal endpoints...or if its a simple function I find its inverse and check that functions domain
Here is another way. The range of a function are all $y$ so that the equation $f(x) = y$ has a solution in the domain.

4. Originally Posted by ThePerfectHacker
Here is another way. The range of a function are all $y$ so that the equation $f(x) = y$ has a solution in the domain.
Yeah that is how I check the possibility for a function to not have an element of the range...but it dose not help me for finding the range...for example I could use that method to check whether or not 1 is in the range by saying $1=f(x)$ and seeing if there is an x value that satisfies that equation...but it doesnt help me to go o well since $f(x)=randomfunction$ then the range is this

5. Originally Posted by Mathstud28
Yeah that is how I check the possibility for a function to not have an element of the range...but it dose not help me for finding the range...for example I could use that method to check whether or not 1 is in the range by saying $1=f(x)$ and seeing if there is an x value that satisfies that equation...but it doesnt help me to go o well since $f(x)=randomfunction$ then the range is this
Here is an example. Let $y=2e^{-x^2}$, the domain is of course all numbers. The range are all $y$ so that we can solve the equation $y=2e^{-x^2}$ for $x$ in the domain. We begin by writing, $(y/2) = e^{-x^2}$ but that can only have a solution if $(y/2) > 0$ (because the exponentinal is positive). Which means if $y/2>0$ then $\ln (y/2) = -x^2 \implies - \ln (y/2) = x^2$. Now to solve this equation we require $- \ln (y/2) \geq 0 \implies \ln (y/2) < 0 \implies 0. For those values we can solve the equation.

Try this example. Find the range of $y = x/(x^2+1)$.