# Thread: natural domain of functions.

1. ## natural domain of functions.

hey..any help would be greatly appreciated. been trying to figure this one out for a quite a while now..

let t(x) = 4x + 3 if x<= -3
4 + 2x - x^2 if -2< x < 2
e^x if x > 2

its a piecewise function im assuming...the question asks....
"Find the natural domain of the function 't'

thanks

2. Originally Posted by b00yeah05
hey..any help would be greatly appreciated. been trying to figure this one out for a quite a while now..

let t(x) = 4x + 3 if x<= -3
4 + 2x - x^2 if -2< x < 2
e^x if x > 2

its a piecewise function im assuming...the question asks....
"Find the natural domain of the function 't'

thanks
what does "natural" domain mean?

i know about the domain, this is simply all the input values we can have.

we have all x less than or equal to -3 covered by the first piece of the function, we have x's that are greater than -2 but less than 2 covered by the second piece, and all x's greater than two covered by the third piece. thus the domain of t(x) is given by:

$\mbox{dom}(t) = (-\infty, 3] \cup (-2,2) \cup (2, \infty)$

3. thanks for your help jhevon. i know how you get those values but im just trying to think of how the working would be showed in order to get those values. any idea??
thanks

4. Originally Posted by b00yeah05
thanks for your help jhevon. i know how you get those values but im just trying to think of how the working would be showed in order to get those values. any idea??
thanks
there is really no working to do here. you just look at what values the function is defined for and restate them...