Answer:
[tex]f(g(f(2)))=22[/tex]
Step-by-step explanation:
The given functions are
[tex]f(x)=x+2[/tex]
and
[tex]g(x)=x^2+4[/tex]
We want to find [tex]f(g(f(2))[/tex].
We first find [tex]f(2)=2+2=4[/tex]
This implies that we are finding [tex]f(g(4)[/tex].
[tex]f(g(x))=f(x^2+4)[/tex]
[tex]\Rightarrow f(g(x))=x^2+4+2[/tex]
[tex]\Rightarrow f(g(x))=x^2+6[/tex]
This implies that;
[tex]\Rightarrow f(g(4))=4^2+6[/tex]
[tex]\Rightarrow f(g(4))=16+6[/tex]
[tex]\Rightarrow f(g(4))=22[/tex]
[tex]\therefore f(g(f(2)))=22[/tex]
