Function composition is applying one function to the results of another:
[tex]\rightarrow g(x)\rightarrow f(x)\rightarrow[/tex]
This means the result of g() is sent through f(). Written notation for the composition is
[tex](f\circ g)(x)=f(g(x)).[/tex]
Note that [tex]g(0)=2,[/tex] then
[tex](f\circ g)(0)=f(g(0))=f(2).[/tex]
Since [tex]f(2)=3,[/tex] then
[tex](f\circ g)(0)=f(2)=3.[/tex]
Answer: [tex](f\circ g)(0)=3.[/tex]
