Answer:
4) The first answer
5) The fourth answer
Step-by-step explanation:
4) When function f is divided by function g, you have:
[tex]\frac{-1}{x\sqrt{3x-9} }[/tex].
Let's first see what will make the denominator 0 to see which values you can't have in the domain.
The first value that comes to mind is 0 since it makes the denominator of [tex]\frac{f}{g} (x)[/tex] equal to 0. Therefore, 0 cannot be a part of the domain.
Another value that comes to mind is 3 because if x = 3, the value under the radical becomes 0 and the denominator of [tex]\frac{f}{g} (x)[/tex] becomes 0. Therefore 3 cannot be part of the domain.
Now we have to consider when the value under the radical is negative since you can't have negative values under the radical. Any number less than 3 will make it negative.
When we combine all this we have that
x ≠ 0, x ≠ 3, and x > 3. Only the first answer meets all 3 of these conditions. Therefore the answer domain is (3, infinity)
5) (f + g)(x) means that you just add the two polynomials. So if we add like terms we have
[tex]x^3 - 2x^2 + 1 + 4x^3 - 5x + 7 = 5x^3 - 2x^2 -5x + 8[/tex]
Therefore the correct answer is the fourth choice.
