Maria lives 98 miles away from her grandparents. She wants to be at her grandparents’ house by 3:00 pm. If she leaves her house
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Given,
The line f and g are parallel lines.
a)The measure of angle 2 is 117 degree.
By exterior atlernate angle property,
The measure of angle 7 is 117 degree.
b)The measure of angle 4 is 68 degree.
By sum of adjacent angle between two parallel lines property,
The measure of angle 6 is 112 degree.
c)The measure of angle 5 is 32 degree.
By alternate interior angle property,
The measure of angle 4 is 32 degree.
d)The measure of angle 7 is 121 degree.
By corresponding angle property,
The measure of angle 3 is 121 degree.
Answer: First, injective means that for every y, there is only one x such f(x) = y, and surjective means that if f is a function that goes from the set {x} to the set {y}, for every element y in the codomain there is at least one element x in the domain such f(x) = y
(a) f:R----> + R given by f(x) = x2 (i guess you written )
The function is not injective, because f(-2) = f(2), and is surjective, because the codomain is +R, and is always a positive real number.
(b) f:N----> + N given by f(n) = n2 (i guess you written )
As the naturals have no negative numbers, in this case the function is injective, but isn't surjective, because there is no number that when squared is equal to 5, for example.
(c) f: Zx Z → Z given by f(n, k) = n +k:
here the domain is of the form (n,k) and the function is n +k, so the numbers (z,w) and (w,z) return the same value when evaluated in f, then f is not injective. And is easy to see that f is surjective, because in the sum you can reach al the integers on the codomain.