If F = { (1,2), (3, 5), (4,7)} and G = { (1,4), (3,0), and (5, 2)}, what is F + G? What is F\G (using function arithmetic)?

Question

If you can, please try and also walk me through the steps along with the answer.

Answer 1

This is the concept of composite functions.There are two functions here: F and G. 

 

For F+G, you focus on adding the second (y) coordinates of both function that correspond to the same element in the domain (x).

 

F+G = {(1, 2+4), (3, (5+0)} = {(1,6), (3,5)}

 

F/G = {(1, 2/4), (3, 5/0)} = {(1,0.5), (3, undefined)}. This means that, the function F/G is not defined at x = 3, that is, there is a vertical asymptote at x = 3.

 

You may ask why points corresponding to x =4 and x = 5 are not included. This is because they are not included simultaneously in F and G above. There is no information on (5,?) in F, and none on (4,?) in G. However, if these two functions were plotted, it may be possible to get this information from each graph. Actually, F+G is a summation of two functions. F/G is the division of function F by function G.

 

I hope this suffices. If you need more help, let me know by contacting wyzant.

Answer 2

(F + G)(x) = F(x) + G(x)

(F + G)(1) = F(1) + G(1) = 2 + 4 = 6

(F + G)(3) = F(3) + G(3) = 5 + 0 = 5

(F + G)(4) = F(4) + G(4) = 7 + 2 = 9

 

(F/G)(x) = F(x)/G(x)

(F/G)(1) = F(1)/G(1) = 2/4 = 1/2

 

Follow the pattern for the other two.