Question

Domain of root(6-x)-root(3x-9)

Answer 1

Answer:

$3\leq x\leq 6$

Step-by-step explanation:

So we want to find the domain of:

$\sqrt{6-x}-\sqrt{3x-9}$

Recall that the radicands cannot be negative. In other words, they must be greater than or equal to 0. So, to solve the domain, determine the restrictions of each radical:

$6-x\geq 0$

Add x to both sides:

$6\geq x$

Flip:

$x\leq 6$

So, for the first radical, x must be less than or equal to 6.

Second radical:

$3x-9\geq 0$

Add 9 to both sides:

$3x\geq 9$

Divide both sides by 3:

$x\geq 3$

So, our domain is:

$x\leq 6\text{ and } x\geq 3$

Therefore, as a compound inequality, this is:

$3\leq x\leq 6$

This is our domain.

And we're done!