Question

What is the domain of the function `f(x)=sqrt(6 - 2x)`?

Answer 1

In this case you do not want a negative argument for the square root (you cannot find the solution of a negative square root, at least as a real number).

What you do it is to "impose" that the argument is always positive or zero (you know the square root of a positive number or zero).

So you set the argument bigger or equal to zero and solve for `x` to find the ALLOWED values of your variable:

`6-2x>=0`
`2x<=6` here I changed sign (and reversed the inequality).

And finally:
`x<=3`

So the values of `x` that you can accept (domain) for your function are all the values smaller than `3` including `3`.
Check by yourself substituting for example `3`, `4` and `2` to confirm our deduction.