We will have the following:
1. f(g(2)):
[tex]g(2)=3(2)-5\Rightarrow g(2)=1[/tex]
[tex]\Rightarrow f(g(2))=2(1)^2+1\Rightarrow f(g(2))=3[/tex]
2. f(g(x)):
[tex]f(g(x))=2(3x-5)^2+1\Rightarrow f(g(x))=2(9x^2-30x+25)+1[/tex]
[tex]\Rightarrow f(g(x))=18x^2-60x+51[/tex]
3. g(f(x)):
[tex]g(f(x))=_{}3(2x^2+1)-5\Rightarrow g(f(x))=6x^2-2[/tex]
4. (g ° g)(x):
[tex](g\circ g)(x)=3(3x-5)-5\Rightarrow(g\circ g)(x)=9x-20[/tex]
5. (f ° f)(x):
[tex](f\circ f)(x)=2(2x^2+1)^2+1\Rightarrow(f\circ f)(x)=2(4x^4+4x^2+1)+1[/tex]
[tex]\Rightarrow(f\circ f)(x)=8x^4+8x^2+3[/tex]
