Answer: g(f(0)) = 2 and (f ° g)(2) = -3.
Step-by-step explanation: We are given the following two functions in the form of ordered pairs :
f = {(-2, 3), (-1, 1), (0, 0), (1,-1), (2,-3)}
g = {(-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)} .
We are to find g(f(0)) and (f ° g)(2).
We know that, for any two functions p(x) and q(x), the composition of functions is defined as
[tex](p\circ q)(x)=p(q(x)).[/tex]
From the given information, we note that
f(0) = 0, g(0) = 2, g(2) = 2 and f(2) = -3.
So, we get
[tex]g(f(0))=g(0)=2,\\\\(f\circ g)(2)=f(g(2))=f(2)=-3.[/tex]
Thus, g(f(0)) = 2 and (f ° g)(2) = -3.
