Question

5. (9) Letf- ((-2, 3), (-1, 1), (0, 0), (1,-1), (2,-3)) and let g- ((-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)j. Find: a. (g f (0) c. (f ° g)(2)

Answer 1

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

$(p\circ q)(x)=p(q(x)).$

From the given information, we note that

f(0) = 0,  g(0) = 2,  g(2) = 2  and  f(2) = -3.

So, we get

$g(f(0))=g(0)=2,\\\\(f\circ g)(2)=f(g(2))=f(2)=-3.$

Thus,  g(f(0)) = 2 and  (f ° g)(2) = -3.