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
![(p\circ q)(x)=p(q(x)).](https://tex.z-dn.net/?f=%28p%5Ccirc%20q%29%28x%29%3Dp%28q%28x%29%29.)
From the given information, we note that
f(0) = 0, g(0) = 2, g(2) = 2 and f(2) = -3.
So, we get
![g(f(0))=g(0)=2,\\\\(f\circ g)(2)=f(g(2))=f(2)=-3.](https://tex.z-dn.net/?f=g%28f%280%29%29%3Dg%280%29%3D2%2C%5C%5C%5C%5C%28f%5Ccirc%20g%29%282%29%3Df%28g%282%29%29%3Df%282%29%3D-3.)
Thus, g(f(0)) = 2 and (f ° g)(2) = -3.