Question

Which pair of functions represents a decomposition of f(g(x)) = | 2(x + 1)^2 + (x + 1) | ?

A) f(x) = (x + 1)^2 and g(x) = | 2x + 1 |
B) f(x) = (x + 1) and g(x) = | 2x^2 + x |
C) f(x) = | 2x + 1 | and g(x) = (x + 1)^2
D) f(x) = | 2x^2 + x | and g(x) = (x + 1)

Answer 1

D

Explanation:

Answer 2

`\Large \boxed{\mathrm{\bold{D.}} \ f(x) = | 2x^2 + x | \ \mathrm{and} \ g(x) = (x + 1)}`

Explanation:

`f(g(x)) = | 2(x + 1)^2 + (x + 1) |`

The first option :

`f(x) = (x + 1)^2 \ \mathrm{and} \ g(x) = | 2x + 1 |`

`f(g(x))=(|2x+1|+1)^2`

The second option :

`f(x) = (x + 1) \ \mathrm{and} \ g(x) = | 2x^2 + x |`

`f(g(x))=(|2x^2 +x|+1)`

The third option :

`f(x) = | 2x + 1 | \ \mathrm{and} \ g(x) = (x + 1)^2`

`f(g(x))=|2(x+1)^2 +1 |`

The fourth option :

`f(x) = | 2x^2 + x | \ \mathrm{and} \ g(x) = (x + 1)`

`f(g(x))= | 2(x + 1)^2 + (x + 1) |`