Question

how do i find the domain of f(x)=-sqrt(6-x-x^2) algebraically?

Answer 1

Within the real numbers you can only take the square root of a non-negative number. So the domain of the function f(x) will be the set of x's for which

\[-x^2-x+6 \ge0\]

Answer 2

can I multiply by -1 in each side so I have all positive numbers (except the 6 which will turn -negative)

Answer 3

Yes, but the inequality will switch direction.

For example: 3 < 5 but if I multiply both sides by -1 I get

-3 > -5