Option A:
[tex]g(f(x))=4x^4+4x^2[/tex]
Solution:
A composite function is created when one function is substituted into another function.
Given [tex]f(x)=2 x^{2}[/tex] and [tex]g(x)=x^{2}+2 x[/tex]
To find which expression represents [tex]g(f(x))[/tex].
Substitute f(x) into the function g(x).
[tex]g(f(x))=g(2x^2)[/tex]
Here [tex]2x^2[/tex] in place of x. So expand it using [tex]g(x)=x^{2}+2 x[/tex].
[tex]=(2x^2)^2+2(2x^2)[/tex]
[tex]=2^2x^4+4x^2[/tex]
[tex]=4x^4+4x^2[/tex]
[tex]g(f(x))=4x^4+4x^2[/tex]
Option B is the correct answer.
Hence [tex]g(f(x))=4x^4+4x^2[/tex].
