Problem in finding functions Domain & Rage of a peacewise function

[sadaf2605]

Homework Statement

Find the domain and range:
{ x+2, x$$\leq$$0
f(x) ={x³, |x|<1
{-x+3, x$$\geq$$1

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$$\leq$$0
f(x) ={x³, |x|<1
{-x+3, x$$\geq$$1

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:
$$\begin{aligned} \text{domain of f(x) } &= (-\infty, -1] \cup (-1, 1) \cup [1, \infty) \\ &= (-\infty, \infty) \end{aligned}$$
(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!