Problem in finding functions Domain & Rage of a peacewise function

[sadaf2605]

Homework Statement

Find the domain and range:
{ x+2, x\leq0
f(x) ={x³, |x|<1
{-x+3, x\geq1

Homework Equations

domain = possible inputs
range = possible outputs

The Attempt at a Solution

domain of f(x) = (-\alpha, -1] \cup (-1, 1) \cup [1, \alpha)
=(-\alpha, \alpha)

range of f(x) = (-\alpha, 1] \cup (-1, 1) \cup [2, \alpha)
= (-\alpha, 1] \cup [2, \alpha)

 

[eumyang]

Homework Statement

Find the domain and range:
{ x+2, x\leq0
f(x) ={x³, |x|<1
{-x+3, x\geq1

Are you sure that the part I bolded isn't -1?

domain of f(x) = (-\alpha, -1] \cup (-1, 1) \cup [1, \alpha)
=(-\alpha, \alpha)

Use "\infty" if you want to display ∞. It's also better to put entire expressions within the tex tags, instead of putting individual symbols within tex tags, like ths:
\begin{aligned}<br /> \text{domain of f(x) } &amp;= (-\infty, -1] \cup (-1, 1) \cup [1, \infty) \\<br /> &amp;= (-\infty, \infty)<br /> \end{aligned}
(Click the expression above to see the code I typed.)

 

[sadaf2605]

Are you sure that the part I bolded isn't -1?

you are right that part would be -1 and i did a lot of typing mistakes, and now help me finding the range of this function!