If f={ (1,2),(3,5),(4,1)} and g= { (2,3), (5,1),(1,3)} , then (gof)=?

(a) { (3,1) , (1,3), (3,4)}
(b) { (1,3) , (3,1), (4,3)}
(c) { (3,4) , (4,3), (1,3)}
(d) { (2,5) , (5,2), (1,5)}

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Work Shown:

The notation "g o f" means g(f(x)). We have f(x) as the inner function that is computed first.

f(x) = {  (1,2),  (3,5), (4,1) }

The x coordinates of each point are: 1, 3, 4

The y coordinates are: 2, 5, 1

So the input x = 1 goes to y = 2 as the output. That output becomes the input of the g(x) function. Using x = 2 as the input for g, we see that 3 is the output. Check out the diagram below to see how each input goes into f, then goes into g to ultimately determine the x,y pairs. So far we've shown that x = 1 ultimately leads to y = 3.

Let's do another input: if x = 3 is plugged into f(x), then the output is 5 because of the point (3,5). Then x = 5 is plugged into g(x) to get x = 5 lead to y = 1. Ultimately x = 3 leads to y = 1 giving us (3,1) as another point.

Lastly, if x = 4 is plugged into f we get y = 1 as an output, which in turn is plugged into g to get 3 as the final output. The point (4,3) is the last ordered pair.

Again there's a lot to keep track of, so it helps to have a diagram as shown below.

ιт ωιℓℓ gσ

5,-10,20,-40,30,-60

нσρє ι ¢συℓ∂ нєℓρ