Evaluate each expression when f = {(-2,1),(0,1),(1,2),(2,3)} and g = {(0,4),(1,2),(2,0),(3,-2)}

Question

Evaluate each expression when f = {(-2,1),(0,1),(1,2),(2,3)} and g = {(0,4),(1,2),(2,0),(3,-2)}

(f°g)(1)

Answer 1

Hello Alyssa!

this expression can be written as f(g(1))

In the statement, f and g were written as several points in a given space. These points are expressed as coordinates x and y (x,y). To each value of x, there is one, and only one value of y. That's what characterizes f and g as functions.

Based on the space represented by g, we can see, from the point (0,4) that g(0) = 4, because, in this case y = g(x). For the same reason, g(1) = 2; g(2) = 0, and g(3) = -2.

Note that, for example g(4) doesn't exist, because 4 is not in the domain of g.

The same reasoning can be applied to the function f, so:

g(1) = 2

f(g(1)) = f(2) = 3