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,+∞)