Question

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

Answer 1

Answer:

D.

$f(x)*g(x)=\frac{x-2}{x+6}$

Explanation:

Given:

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

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

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

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