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Lilit [14]
3 years ago
8

Determine if each of the examples below are functions or not. If a given construction is not a function, prove it by showing tha

t a single input can have multiple outputs (not well defined) or that some input doesn't have an output (not total). If it is a function, show it by showing each input has exactly one output.
a) f : R \ {0} -----> R such that f(x) = x^-1
b) f : R -----> R such that f(x) = y iff y <_ x
c) f : Compound Propositions -------> {T,F} such that f(x) = T if x is satisfiable, and f(x) = F otherwise.
Mathematics
1 answer:
sveticcg [70]3 years ago
5 0

Answer:

A. Not a function

B. It is a function

C. Not a function

Step-by-step explanation:

A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to.

So let check each of the function given.

a. f(x)=x^-1

i.e f(x)= 1/x

Let take a look at the function (1/x) at negative infinity it will have 0 and at positive infinity it will have 0- too.

Therefore it is continuous at both positive and negative infinity

Observe that 1/x→x+∞ as x→0+ and 1/x→x−∞ as x→0−.

Now at x=0 is is infinity and it is not continuous at that point.

Therefore the function is continuous on the real axis except at 0....

If we consider all the points then it is not continuous

b. f(y)= x for y≤x

This is a function because for every value of y there is a unique value of x

1 to 1

2 to 2

3 to 3

And so on

A there is one value for x and y.

Therefore it is a function

c. Given that f(x)= T

And also f(x) = F

This is not a function because a value from the domain has two different value from the range

So it doesn't have a unit value, value x from the domain has two different value F and T from the range.

Then it is not a function. .

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Assume that the probability of a defective computer component is 0.02. Components arerandomly selected. Find the probability tha
solmaris [256]

Answer:

0.0177 = 1.77% probability that the first defect is caused by the seventh component tested.

The expected number of components tested before a defective component is found is 50, with a variance of 0.0208.

Step-by-step explanation:

Assume that the probability of a defective computer component is 0.02. Components are randomly selected. Find the probability that the first defect is caused by the seventh component tested.

First six not defective, each with 0.98 probability.

7th defective, with 0.02 probability. So

p = (0.98)^6*0.02 = 0.0177

0.0177 = 1.77% probability that the first defect is caused by the seventh component tested.

Find the expected number and variance of the number of components tested before a defective component is found.

Inverse binomial distribution, with p = 0.02

Expected number before 1 defective(n = 1). So

E = \frac{n}{p} = \frac{1}{0.02} = 50

Variance is:

V = \frac{np}{(1-p)^2} = \frac{0.02}{(1-0.02)^2} = 0.0208

The expected number of components tested before a defective component is found is 50, with a variance of 0.0208.

5 0
2 years ago
If anyone knows the answer to these can u please help? thank you! :)
Dennis_Churaev [7]

Answers:

  • A) Ray QS or Ray QR
  • B)  Line segment QS or SQ
  • C)  Plane QSR
  • D)  Line QS or RQ

=======================================================

Explanation:

Part A)

When naming a ray, always start at the endpoint. This is the first letter and we'll start with point Q.

The second letter is the point that is on the ray where the ray aims at. We have two choices S and R as they are both on the same ray. That's why we can name this Ray QS and Ray QR.

--------------------

Part B)

A segment is named by its endpoints. The order of the endpoints doesn't matter so that's why segment QS is the same as segment SQ. To me, it seems more natural to read from left to right, so QS seems better fitting (again the order doesn't matter).

--------------------

Part C)

When forming a plane, you need 3 noncollinear points. The term "collinear" means the points all fall on the same line. So these three points cannot all fall on the same straight line. In other words, we must be able to form a triangle of some sort.

So that's how we get the name "Plane QSR". The order of the letters doesn't matter.

--------------------

Part D)

To name a line, we just need to pick two points from it. Any two will do. The order doesn't matter. So that's how we get Line QS and Line RQ as two aliases for this same line. It turns out that there are 6 different ways to name this line.

  1. Line QR
  2. Line QS
  3. Line RQ
  4. Line RS
  5. Line SQ
  6. Line SR
4 0
2 years ago
Bryce lives 26 miles from his grandmother's house .how many kilometers does bryce live from his grandmother's house? round your
faltersainse [42]
He lives roughly 41.8 kilometers away from his grandma's house
8 0
2 years ago
Read 2 more answers
Recall the equation for a circle with center ( h , k ) (h,k) and radius r r. At what point in the first quadrant does the line w
garri49 [273]
Equation of this circle is
x^2 + (y - 2)^2 = 36
y = 2.5x + 2

Substitute for y in the equation of the circle:-

x^2 + (2.5x + 2 - 2)^2 = 36

x^2 + 6.25x^2 = 36

x^2 = 36 / 7.25  

x = +/-   6  /  2.693  =  +/- 2.228

when x = 2.228 y = 2.5(2.228) + 2 =  7.57    to nearest hundredth

when x = -2.228 y = 2.5(-2.228) + 2 =   -3.57

So they intersect at 2 points but the intersect in the first quadrant is at (2.23, 7,57)        to nearest hundredth.
7 0
3 years ago
Factor the polynomial function.<br> G(v) - 196v² + 100
miskamm [114]

Answer:

4(49v²+25)

Step-by-step explanation:

196 {v}^{2}  + 100

4(49 {v}^{2}  + 25)

3 0
2 years ago
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