Question

I know this isn't the subject of math, but nobody can answer it in math and I need help with the steps because I need to turn it in I know the answer I just need help with the steps please and thank you! Btw the correct answer is A

Answer 1

F(x)=-1/x
g(x)=√(3x-9)

Domain of (f/g)(x):  ??

1We find out the domain of f(x):
f(x) is a rational function, therefore can take real values if the denominator is not ("0"), therefore the domain of f, will be all values excpet "0"
Domain of  f: (-∞,0)U(0,+∞); 


                                                          o
----------------------------------------------O-------------------------------------------
←-------- -∞                                                               +∞           ----------→


g(x) is a radical square root  function, therefore the radicand have to be greater than o equal to "0"
3x-9≥0
3x≥9
x≥3

                                                         3
.........................................................Ф--------------------------------
←--------- - ∞                                                        +∞ -----------→
          
(f/g)(x) = (-1/x) / (√(3x-9)) is a rational function with a square root in the denominator,also the square root don´t take the value of "0";
Therefore:
3x-9>0
3x>9
x>3

The domain of the function (f/g)(x) only can take the values found in all three domains at once.
                                                            3
............................................................0---------------------------------
←--------- -∞                                                          +∞-------------→

Answer: (3,+∞)