Determine the domain of the function.

Question

anonymous · Answer

$$f(x)=\sqrt{11-x}$$

xapproachesinfinity · Answer

the domain should be $$11-x\ge 0 \Longrightarrow x\le11$$

xapproachesinfinity · Answer

that means all the real numbers less than 11

anonymous · Answer

So the idea is that it cant equal zero?

xapproachesinfinity · Answer

no it can't be negative 
zero is okay under the root

anonymous · Answer

Oh okay...Thanks!

xapproachesinfinity · Answer

WC!

anonymous · Answer

I have one more similar question if you dont mind

anonymous · Answer

$$\frac{ \sqrt{x+3} }{ (x+8)(x-2)}$$

anonymous · Answer

What would the domain be here?

xapproachesinfinity · Answer

well this one you have two thing to take care off
the first is the root we don't want negative numbers under it
the second the denominator we don't want zero there (something over zero is not good)
so saying that we have to set those conditions
$$x+3\ge0 ~and~ x+8\ne0,  ~ x-2\ne0$$

xapproachesinfinity · Answer

you solve for each one and then see the intersections

nevermind_justschool · Answer

That's a great way of explaining it... 
|(^)_(~)|

anonymous · Answer

I understand how you explained that so now if my answer choices are 
a. All real numbers except -8, -3 and 2
b. $$x \ge 0$$
c. all real numbers 
 d. $$x \ge -3, x \neq 2$$

anonymous · Answer

a

xapproachesinfinity · Answer

to make it easier for you
$$x\ge -3 ~and~ x\ne -8 ~and~ x\ne2$$
now writing this into the interval notation
$$\ [-3, \infty) \cap[ (-\infty , -8)\cup (-8,2)\cup(2, \infty)$$

xapproachesinfinity · Answer

look for this intersection

xapproachesinfinity · Answer

you might one to draw a number line
see where they overlap

anonymous · Answer

Thank you! I get it

xapproachesinfinity · Answer

no problem :)