Question

According to the table what is the value of (f+g)(2)?

Answer 1

(f o g)(x) means:

`(f\circ g)(x)=f(g(x))`

That is a nested function, where the input of the function f is the output of function g.

Then, we can construct the result (output) for this nested function for x from 0 to 3:

`\begin{gathered} x=0\longrightarrow g(0)=2\longrightarrow f(2)=1\longrightarrow(f\circ g)(0)=1 \\ x=1\longrightarrow g(1)=3\longrightarrow f(3)=2\longrightarrow(f\circ g)(1)=2 \\ x=2\longrightarrow g(2)=0\longrightarrow f(0)=3\longrightarrow(f\circ g)(2)=3 \\ x=3\longrightarrow g(3)=1\longrightarrow f(1)=0\longrightarrow(f\circ g)(3)=0 \end{gathered}`