Step-by-step explanation:
(a)
Using the definition given from the problem
![f(A) = \{x^2 \, : \, x \in [0,2]\} = [0,4]\\f(B) = \{x^2 \, : \, x \in [1,4]\} = [1,16]\\f(A) \cap f(B) = [1,4] = f(A \cap B)\\](https://tex.z-dn.net/?f=f%28A%29%20%3D%20%5C%7Bx%5E2%20%20%5C%2C%20%3A%20%5C%2C%20x%20%5Cin%20%5B0%2C2%5D%5C%7D%20%3D%20%5B0%2C4%5D%5C%5Cf%28B%29%20%3D%20%5C%7Bx%5E2%20%20%5C%2C%20%3A%20%5C%2C%20x%20%5Cin%20%5B1%2C4%5D%5C%7D%20%3D%20%5B1%2C16%5D%5C%5Cf%28A%29%20%5Ccap%20f%28B%29%20%3D%20%5B1%2C4%5D%20%20%3D%20f%28A%20%5Ccap%20B%29%5C%5C)
Therefore it is true for intersection. Now for union, we have that
![A \cup B = [0,4]\\f(A\cup B ) = [0,16]\\f(A) = [0,4]\\f(B)= [1,16]\\f(A) \cup f(B) = [0,16]](https://tex.z-dn.net/?f=A%20%5Ccup%20B%20%3D%20%5B0%2C4%5D%5C%5Cf%28A%5Ccup%20B%20%29%20%3D%20%5B0%2C16%5D%5C%5Cf%28A%29%20%3D%20%5B0%2C4%5D%5C%5Cf%28B%29%3D%20%5B1%2C16%5D%5C%5Cf%28A%29%20%5Ccup%20f%28B%29%20%3D%20%5B0%2C16%5D)
Therefore, for this case, it would be true that
.
(b)
1 is not a set.
(c)
To begin with
![A\cap B \subset A,B](https://tex.z-dn.net/?f=A%5Ccap%20B%20%5Csubset%20A%2CB)
Therefore
![g(A\cap B) \subset g(A) \cap g(B)](https://tex.z-dn.net/?f=g%28A%5Ccap%20B%29%20%5Csubset%20g%28A%29%20%5Ccap%20g%28B%29)
Now, given an element of
it will belong to both sets, therefore it also belongs to
, and you would have that
, therefore
.
(d)
To begin with
, therefore
![g(A) \cup g(b) \subset g(A\cup B)](https://tex.z-dn.net/?f=g%28A%29%20%5Ccup%20g%28b%29%20%5Csubset%20g%28A%5Ccup%20B%29)
Answer:
-9 and 3
Step-by-step explanation:
as -9×3= -27
and
-9+3= -6
15: M= 2
B= -5
Slope intercept form= y=2x-5
16: y=5/8x + 1/2
A-b
difference means subtract
Answer:
The man covers 200 ft in 40 seconds.
Step-by-step explanation:
A person is moving on the sidewalk from one end to the other end.
He walks 40 feet in 8 seconds.
Therefore his speed = ![\frac{distance covered}{time}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20covered%7D%7Btime%7D)
= ![\frac{40}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B8%7D)
= 5 ft/![s^{2}](https://tex.z-dn.net/?f=s%5E%7B2%7D)
He covers the sidewalk distance at a rate of 5 feet every second.
To calculate the time taken to cover 200 ft,
time = ![\frac{distance to be covered}{speed}](https://tex.z-dn.net/?f=%5Cfrac%7Bdistance%20to%20be%20covered%7D%7Bspeed%7D)
time =![\frac{200}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7B5%7D)
<u>time = 40 seconds</u>
Hence the man covers 200 ft in 40 seconds.