Answer:
the answer is option E.
Explanation:
it is in the form f/g (x).
we know f and g from the equation;
we can rewrite it as, (√(9-x^2)/(3x-1))
if you notice you cannot put any number less than -3 or greater than 3 in the numeror because if you do you get a negative root which is false. for instance if you put 4 or -4 in the numerator you get 9 - (4 or -4 square ) which is 9- 16 which is a negative number and you cannot take root of a negative number.
on the numerator if you put 1/3 as the value for x you will get zero in the denominator. and any number divided by zero is undefined so that cannot be.
this means that option E is the right one that satisfies the condition. it means the domain is [-3, 1/3) U (1/3, 3] .