Find the domain of (f/g)(x) where f(x)= sqrt(x+2) and g(x)= sqrt(3-x).

, i looked it up and it said the answer is [-2,3), but shouldn't -2 not be included because f(-2) would make the square root be 0?

Step-by-step explanation:

(f/g)(x) = √(x+2) / √(3−x)

As you said, f(-2) = 0, but since it's in the numerator, that's okay.

g(3) = 0, and you can't divide by 0, so x=3 is not included.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

t= half of the arc subtended by t.

r= half of the arc subtended by r.  

t+r= half of the arc subtended by t + half of the arc subtended by r= half of 360=180

step-by-step explanation: