Question

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

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step 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 :

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

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