Find the domain on the function.
Write your answer in interval notation. If the answer includes more than one interval write the intervals separated by the union symbol, U.

Question

Find the domain on the function.
 Write your answer in interval notation. If the answer includes more than one interval write the intervals separated by the union symbol, U.

anonymous · Answer

f(x)=sqrt(73.5-7x)

noelgreco · Answer

What limits the domain when you have an even root?  In other words, what has to be true of the radicand, assuming the domain is the set of real numbers?

anonymous · Answer

I have no idea how to even start... Idk...

anonymous · Answer

It cannot be zero right?

noelgreco · Answer

Bingo!  How can you figure out the value of x that makes the radicand (the expression under the radical) = 0?

noelgreco · Answer

Actually, it can be zero, it can't be negative.

noelgreco · Answer

73.5 - 7x = 0.  Solve, but you're not done.

hero · Answer

$\sqrt{0} = 0$

anonymous · Answer

do I solve 73.5-7x=0?

hero · Answer

You find the domain by solving $73.5 - 7x \ge 0$

noelgreco · Answer

It's easiest to solve the equality and then consider  whether an increasing or decreasing value of x satisfies the inequality.