Question

Select the correct answer. Consider functions f and g. (Refer to image) Which expression is equal to f(x) * f(g)?

Answer 1

D.

`f(x)*g(x)=(x-2)/(x+6)`

Step-by-step explanation:

Given:

Let's go ahead and simplify each of the functions as seen below;

`\begin{gathered} f(x)=(x+12)/(x^2+4x-12) \\ =(x+12)/(x^2+6x-2x-12) \\ =(x+12)/(x(x+6)-2(x+6)) \\ =(x+12)/((x+6)(x-2)) \end{gathered}`
`\begin{gathered} g(x)=(4x^2-16x+16)/(4x+48) \\ =(4(x^2-4x+4))/(4x+48) \\ =(4(x^2-2x-2x+4))/(4x+48) \\ =(4[x(x-2)-2(x-2))/(4x+48) \\ =(4[(x-2)(x-2)])/(4(x+12)) \\ =((x-2)^2)/(x+12) \end{gathered}`

Let's go ahead and multiply f(x) and g(x);

`\begin{gathered} f(x)*g(x)=(x+12)/((x+6)(x-2))*((x-2)^(2))/(x+12) \\ f(x)*g(x)=(x-2)/(x+6) \end{gathered}`