Question

Give an example of a function with a domain of (-infinity,0)

Answer 1

You may consider a function with domain
`(0,\infty)` and switch
`x\mapsto -x`

For example, we know that

`y=\log(x)`

can only be evaluated for positive values of the argument. This means that

`y=\log(-x)`

can also be evaluated only for positive values of the argument, i.e.

`-x>0 \iff x<0 \iff x \in (0,\infty)`

To give another example, you may consider a function with domain
`[0,\infty)`, consider its inverse to remove 0 from the domain, and finally switch again
`x\mapsto -x`:

`√(x) \implies D = [0,\infty)\\(1)/(√(x)) \implies D = (0,\infty)\\ (1)/(√(-x)) \implies D = (-\infty,0)`