H(x) = x^2 + 2 - x
g(x) = 4x + 5
find (h - g) (x/3)

 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.

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