Calculating functions

Question

Let the function f be defined by

f = {(-3, 4),(-2, 2), (-1, 0), (0,1), (1, 3), (2, 4), (3, -1)}

and let the function g be defined by

g = {(-3, -2), (-2, 0), (-1, -4), (0, 0), (1, -3), (2, 1), (3, 2)}

Compute the indicated value if it exists.

a. compute (f+g)(-3). What does this answer mean in relation to the two functions?

b. compute (f-g)(2). Why does it matter which order we subtract the functions? What changes occur if we subtract f from g or (g-f)(2)?

c. compute (fg)(-1). Explain your reasoning in this answer.

d. compute (gf)(-3). Does it matter which order we multiply in?

 

Answer 1

This is solved by simply applying the definition of function operators.

a. (f+g)(-3) = f(-3) + g(-3) = 2.

b. (f-g)(2) = f(2) - g(2) = 5

(g-f)(2) = g(2) - f(2) = -3

c. (fg)(-1) = f(g(-1)) = f(-4) which is undefined

d. (gf)(-3) = g(f(-3)) = g(4) which is undefined

(fg)(-3) = f(g(-3)) = f(-2) = 2