Answer:
x^2 - 15x - 27
---------------------- (Answer C)
9
Step-by-step explanation:
(h - g)(x) is the difference between funcions h and g. Subtract g(x) from h(x) as follows:
x^2 + 2 - x
-(4x + 5)
-------------------
x^2 - 5x - 3 = (h - g)(x)
To find (h - g)(x/3), substitute x/3 for x in x^2 - 5x - 3 = (h - g)(x), obtaining:
(x/3)^2 - 5(x/3) - 3
We must expand this and then combine like terms:
x^2/9 - (5/3)x - 3
The LCD of these three terms is 9. The first term stays as is. The second term becomes (15/9)x. The third term becomes 27/9.
Combining these three terms, all with denominator 9, we get:
x^2 - 15x - 27
----------------------
9
This matches Answer C.
