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
HELP Pleasee!!
I'm Clueless :/
Don't worry, I'll guide you step by step to find the solutions to your questions!
First, let's understand the given information. We have three sets of ordered pairs: f, g, and h.
- f = (1,2), (2,3), (3,4), (4,5)
- g = (1,-2), (3,-3), (5,-5)
- h = (1,0), (2,1), (3,2)
Now, let's solve each question one by one:
2a. To find 2a.f+g, we need to multiply each element in f by 2, then add the corresponding elements from g. Let's perform the calculations:
2a.f+g = (2*1 + 1*-2), (2*2 + 3*-2), (2*3 + 4*-3), (2*4 + 5*-5)
= (2 - 2), (4 - 6), (6 - 12), (8 - 25)
= (0, -2, -6, -17)
The domain of 2a.f+g is the set of x-coordinates from f (as they are used in the calculation). So, the domain is {1, 2, 3, 4}.
2b. To find 2b.f-g, we need to multiply each element in f by 2, then subtract the corresponding elements from g. Let's perform the calculations:
2b.f-g = (2*1 - 1*-2), (2*2 - 3*-2), (2*3 - 4*-3), (2*4 - 5*-5)
= (2 + 2), (4 + 6), (6 + 12), (8 + 25)
= (4, 10, 18, 33)
The domain of 2b.f-g is the set of x-coordinates from f (as they are used in the calculation). So, the domain is {1, 2, 3, 4}.
2c. To find 2c.f*g, we need to pairwise multiply the corresponding elements from f and g. Let's perform the calculations:
2c.f*g = (1 * 1, 2 * -2), (2 * 3, 3 * -3), (3 * 5, 4 * -5)
= (1, -4), (6, -9), (15, -20)
The domain of 2c.f*g is the set of x-coordinates present in both f and g. So, the domain is {1, 2, 3}.
2d. To find 2d.f/h, we need to divide each element in f by the corresponding elements from h. Let's perform the calculations:
2d.f/h = (1/1, 2/0), (2/2, 3/1), (3/3, 4/2), (4/0, 5/0)
= (1, undefined), (1, 3), (1, 2), (undefined, undefined)
The domain of 2d.f/h is the set of x-coordinates from f for which the divisor is not zero (to avoid division by zero). So, the domain is {1, 2, 3}.
2e. To find G o F o h (G composed with F composed with h), we need to perform the operations from right to left. Let's first compute F o h:
F o h: For each ordered pair in f, we replace the x-coordinate with the corresponding y-coordinate from h.
(1,2) -> (1, 0)
(2,3) -> (2, 1)
(3,4) -> (3, 2)
(4,5) -> (4, undefined)
Next, we compute G o (F o h):
G o (F o h): For each ordered pair in F o h, we replace the x-coordinate with the corresponding y-coordinate from G.
(1,0) -> (0, 0)
(2,1) -> (-3, 1)
(3,2) -> (-5, -5)
(4,undefined) -> undefined
Therefore, the resulting composition G o F o h is: {(0, 0), (-3, 1), (-5, -5), undefined}
The domain of G o F o h is the set of x-coordinates from F o h. So, the domain is {1, 2, 3, 4}.
I hope this explanation helps you understand how to find the solutions and domains for each question. Let me know if you have any further queries!