Answer:
[tex]\Large \boxed{\mathrm{\bold{D.}} \ f(x) = | 2x^2 + x | \ \mathrm{and} \ g(x) = (x + 1)}[/tex]
Step-by-step explanation:
[tex]f(g(x)) = | 2(x + 1)^2 + (x + 1) |[/tex]
The first option :
[tex]f(x) = (x + 1)^2 \ \mathrm{and} \ g(x) = | 2x + 1 |[/tex]
[tex]f(g(x))=(|2x+1|+1)^2[/tex]
The second option :
[tex]f(x) = (x + 1) \ \mathrm{and} \ g(x) = | 2x^2 + x |[/tex]
[tex]f(g(x))=(|2x^2 +x|+1)[/tex]
The third option :
[tex]f(x) = | 2x + 1 | \ \mathrm{and} \ g(x) = (x + 1)^2[/tex]
[tex]f(g(x))=|2(x+1)^2 +1 |[/tex]
The fourth option :
[tex]f(x) = | 2x^2 + x | \ \mathrm{and} \ g(x) = (x + 1)[/tex]
[tex]f(g(x))= | 2(x + 1)^2 + (x + 1) |[/tex]
