Question

Let the functions F:W=x√-x-2 where W={-1,0,2,5,11}

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the values of the function F for each element in the set W, we substitute each element into the given function:

For x = -1:
F(-1) = (-1)√(-1) - 2 = (-1)i - 2 = -1 - 2 = -3

For x = 0:
F(0) = (0)√(0) - 2 = 0 - 2 = -2

For x = 2:
F(2) = (2)√(2) - 2 = (2)(√2) - 2

For x = 5:
F(5) = (5)√(5) - 2 = (5)(√5) - 2

For x = 11:
F(11) = (11)√(11) - 2 = (11)(√11) - 2

Since these last three expressions involve irrational numbers and cannot be simplified further, we leave them in this form.

Answer 2

Explain in details I don't understand I'm writing test by tomorrow so please explain how understand so that I don't fail my test

Answer 3

[AI-generated answer — Bot GPT 3.5]

Certainly! Let's go through each calculation step by step to help you understand.

For x = -1:
We substitute -1 into the function F: W = x√(-x) - 2
F(-1) = (-1)√(-(-1)) - 2
Since -(-1) is equal to 1, we have:
F(-1) = (-1)√1 - 2
The square root of 1 is 1, so we get:
F(-1) = (-1)(1) - 2
Multiplying -1 by 1 gives us -1, so we have:
F(-1) = -1 - 2
Adding -1 to -2 gives us -3:
F(-1) = -3

For x = 0:
We substitute 0 into the function F: W = x√(-x) - 2
F(0) = (0)√(-(0)) - 2
Since -(0) is equal to 0, we have:
F(0) = (0)√0 - 2
The square root of 0 is 0, so we get:
F(0) = (0)(0) - 2
Multiplying 0 by 0 gives us 0, so we have:
F(0) = 0 - 2
Subtracting 2 from 0 gives us -2:
F(0) = -2

For x = 2:
We substitute 2 into the function F: W = x√(-x) - 2
F(2) = (2)√(-(2)) - 2
Since -(2) is equal to -2, we have:
F(2) = (2)√(-2) - 2
The square root of -2 is an irrational number (√(-2)), and it cannot be simplified further. So, we keep it as is as:
F(2) = (2)(√2) - 2

For x = 5:
We substitute 5 into the function F: W = x√(-x) - 2
F(5) = (5)√(-(5)) - 2
Since -(5) is equal to -5, we have:
F(5) = (5)√(-5) - 2
The square root of -5 is an irrational number (√(-5)), and it cannot be simplified further. So, we keep it as is as:
F(5) = (5)(√5) - 2

For x = 11:
We substitute 11 into the function F: W = x√(-x) - 2
F(11) = (11)√(-(11)) - 2
Since -(11) is equal to -11, we have:
F(11) = (11)√(-11) - 2
The square root of -11 is an irrational number (√(-11)), and it cannot be simplified further. So, we keep it as is as:
F(11) = (11)(√11) - 2

I hope this detailed explanation helps you understand how to calculate the function for each element in the set. Good luck with your test!

Answer 4

I don't understand this is not the way I was taught according to new general mathematics s.s.s1

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize if my previous explanation did not align with your understanding. To clarify, let's go through the problem again using a different approach.

The given function is F: W = x√(-x) - 2, where W = {-1, 0, 2, 5, 11}.

For each element in the set W, we substitute the respective values into the function and evaluate:

For x = -1:
F(-1) = (-1)√(-(-1)) - 2 = (-1)√(1) - 2
√(1) is equal to 1, so we have:
F(-1) = -1(1) - 2 = -1 - 2 = -3

For x = 0:
F(0) = (0)√(-(0)) - 2 = (0)√(0) - 2
The square root of 0 is 0, so we get:
F(0) = (0)(0) - 2 = 0 - 2 = -2

For x = 2:
F(2) = (2)√(-(2)) - 2 = (2)√(-2) - 2
√(-2) is an irrational number and cannot be simplified further. So, we keep it as √(-2) in the equation:
F(2) = (2)√(-2) - 2 = 2√(-2) - 2

For x = 5:
F(5) = (5)√(-(5)) - 2 = (5)√(-5) - 2
√(-5) is also an irrational number and cannot be simplified:
F(5) = (5)√(-5) - 2 = 5√(-5) - 2

For x = 11:
F(11) = (11)√(-(11)) - 2 = (11)√(-11) - 2
Again, √(-11) is an irrational number and cannot be simplified:
F(11) = (11)√(-11) - 2 = 11√(-11) - 2

This should provide the correct representation of the function F for the given set.

Answer 6

Infact don't worry this explanation even worse the case I want to ask another question

Explain types of mapping in further mathematics

Answer 7

[AI-generated answer — Bot GPT 3.5]

Certainly! In further mathematics, there are several types of mappings that are commonly studied. These include:

1. One-to-One Mapping or Injective Mapping: In this type of mapping, each element in the domain is mapped to a unique element in the codomain. It means that no two distinct elements in the domain are mapped to the same element in the codomain.

2. Onto Mapping or Surjective Mapping: In this type of mapping, every element in the codomain has at least one element in the domain that maps to it. In other words, every element in the codomain is covered or reached by the mapping.

3. One-to-One Correspondence or Bijective Mapping: This is a combination of both one-to-one and onto mappings. In this type of mapping, each element in the domain is mapped to a unique element in the codomain, and every element in the codomain is covered or reached by the mapping. It establishes a one-to-one correspondence between the elements of the domain and the elements of the codomain.

4. Many-to-One Mapping: In this type of mapping, multiple elements in the domain are mapped to the same element in the codomain. It means that different elements in the domain can be mapped to one common element in the codomain.

These types of mappings are important concepts in further mathematics as they help understand the relationships and connections between sets and their elements. They have various applications in various branches of mathematics, such as algebra, calculus, and discrete mathematics.