Question

Complete the missing portion of the equation.

f(x) = 1/x^2 and g(x) =1/2x+4
f[g(x)] = 4x^2 _______
+ 16x + 16
+ 8x + 16
+16

Answer 1

The missing portion is + 16x + 16.

Explanation:

In order to get
`f(g(x))`, we put

`g(x)= (1)/(2x+4)`

into

`f(x)= (1)/(x^2)`,

which gives us

`f(g(x))= (1)/((g(x) )^2)`

`f(g(x))= (1)/(((1)/(2x+4) )^2)`

`f(g(x))= (2x+4)^2`

we expand and get:

`f(g(x))= 4x^2+16x+16`.

Thus, we see that the missing portion is
`16x+16.`