Answer:
The missing portion is + 16x + 16.
Step-by-step explanation:
In order to get [tex]f(g(x))[/tex], we put
[tex]g(x)= \dfrac{1}{2x+4}[/tex]
into
[tex]f(x)= \dfrac{1}{x^2}[/tex],
which gives us
[tex]f(g(x))= \dfrac{1}{(g(x) )^2}[/tex]
[tex]f(g(x))= \dfrac{1}{(\dfrac{1}{2x+4} )^2}[/tex]
[tex]f(g(x))= (2x+4)^2[/tex]
we expand and get:
[tex]f(g(x))= 4x^2+16x+16[/tex].
Thus, we see that the missing portion is [tex]16x+16.[/tex]
