HELP?
f = (1, 2), (2, 3), (3, 4), (4, 5),
g = (1, -2), (3, -3), (5, -5), and
h = (1, 0), (2, 1), (3, 2),
Find the following and state the domain?!
2a.f+g
2b.f-g
2c. f*g
2d. f/h
2e. G o F o h
To find the following expressions and state the domain, we need to understand the operations being performed on the given sets.
The given sets are:
f = {(1, 2), (2, 3), (3, 4), (4, 5)}
g = {(1, -2), (3, -3), (5, -5)}
h = {(1, 0), (2, 1), (3, 2)}
Let's go step by step:
2a. 2a.f + g
To calculate 2a.f, we multiply each element of f by 2a.
2a.f = {(2a, 2 * 2a), (2a, 2 * 3), (2a, 2 * 4), (2a, 2 * 5)}
Now, we add g to the result of 2a.f.
(2a.f + g) = {(2a + 1, 4a + (-2)), (2a + 3, 4a + (-3)), (2a + 5, 4a + (-5))}
The domain for this expression would be the values of 'a' that allow all the resulting tuples to be valid.
2b. 2b.f - g
To calculate 2b.f, we multiply each element of f by 2b.
2b.f = {(2b, 2 * 2b), (2b, 2 * 3), (2b, 2 * 4), (2b, 2 * 5)}
Now, we subtract g from the result of 2b.f.
(2b.f - g) = {(2b - 1, 4b - (-2)), (2b - 3, 4b - (-3)), (2b - 5, 4b - (-5))}
The domain for this expression would be the values of 'b' that allow all the resulting tuples to be valid.
2c. f * g (f composed with g)
To calculate f * g, we need to match the common elements in both sets based on the first element (1, 3, and 5).
f * g = {(1, 2 * (-2)), (3, 4 * (-3)), (5, -5)}
The domain for this expression would be the values of 'x' for which the resulting tuples are valid.
2d. f / h (f divided by h)
To calculate f / h, we need to match the common elements in both sets based on the first element (1, 2, and 3).
f / h = {(1, 2 / 0), (2, 3 / 1), (3, 4 / 2)}
The domain for this expression would be the values of 'x' for which the resulting tuples are valid. However, we can see that the tuple (1, 2 / 0) is invalid since division by zero is not defined. Therefore, in this case, the domain would exclude x = 1.
2e. g o f o h (g composed with f composed with h)
To find g o f o h, we need to perform function composition by matching the elements in h with f first, and then matching the elements in the resulting set with g.
g o f o h = g o (f o h)
(f o h) = {(1, 2), (2, 3), (3, 4)}
(g o f o h) = {(1, -2), (2, -3), (3, -5)}
The domain for this expression would be the values of 'x' for which the resulting tuples are valid.
Please note that the exact domain values will depend on the specific requirements or constraints defined for 'a,' 'b,' or 'x'.