Answer:
Part a) Domain of f : {-3, -2, -1, 0, 1, 2, 3}
Part b) Domain of g : {-1, 0, 1, 2, 3, 4}
Part c) Domain of f+g = {-1, 0, 1, 2, 3}
Part d) Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}
Step-by-step explanation:
Part a) Determining the domain of f
Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}
Domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.
Domain of f : {-3, -2, -1, 0, 1, 2, 3}
Part b) Determining the domain of g
Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}
As domain is the set of the input values of x which define the function. In other words, domain is the set of all the first elements of order pairs.
Domain of g : {-1, 0, 1, 2, 3, 4}
Part c) Determining the domain of f+g
When there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains.
As,
Given f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}
Domain of f : {-3, -2, -1, 0, 1, 2, 3}
and,
Given g= {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}
Domain of g : {-1, 0, 1, 2, 3, 4}
As when there is a sum of two functions f and g, then domain of f+g will be the intersection of their domains
So, the domain of f+g = {-1, 0, 1, 2, 3}
Part d) List the ordered pairs of f-g
As
f = {(-3,40),(-2,25),(-1,14),(0,7),(1,4),(2,5),(3,7)}
and
g = {(-1,4),(0,5),(1,6),(2,1),(3,-16),(4,-51)}
For f - g, we must focus on subtracting the second (y) coordinates of both function that correspond to the same element in the domain (x)
(f - g)(x) = f(x) - g(x)
(f - g)(x) = f(-1) - g(-1) = 14 - 4 = 10
(f - g)(x) = f(0) - g(0) = 7 - 5 = 2
(f - g)(x) = f(1) - g(1) = 4 - 6 = -2
(f - g)(x) = f(2) - g(2) = 5 - 1 = 4
(f - g)(x) = f(3) - g(3) = 7 - (-16) = 23
So,
Ordered Pairs of f-g = {(-1, 10), (0, 2), (1, -2), (2, 4), (3, 23)}
Keywords: domain, function, f+g, f-g
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