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Stella [2.4K]
2 years ago
6

1. what are the domain and range of the function?

Mathematics
2 answers:
natta225 [31]2 years ago
7 0

1) domain of the first is ( R ) because of its root(3) and its range is (R) because of its root again

2)and domain of the last , is [0,+infinity)

and for its range , you can draw it such as picture and will be [0,- infinity)

Allisa [31]2 years ago
3 0

Answer:

1. Dom(f)=\mathbb{R}, Ran(f)=\mathbb{R}.

2. Dom(f)=\{x\in \mathbb{R} : x\geq 0 \}, Ran(f)=\{x\in \mathbb{R} : x \leq 0 \}.

Step-by-step explanation:

1. Since the degree of the radical is an odd number, the radicand can be any real number, then x can take any real value, so the domain of f is the set of all real numbers, \mathbb{R}.

Now, if x\in \mathbb{R} , then x-3 \in \mathbb{R}, so  \sqrt[3]{x-3} \in \mathbb{R}, and thus f(x)\in \mathbb{R}, which leads us to affirm that the range of  f  is the set of all real numbers, \mathbb{R}.

2. Since the degree of the radical is an even number, the radicand can not be a negative number, then x can take only nonnegaive values, so the domain of f is the set of all nonnegative numbers, \{x\in \mathbb{R} : x\geq 0 \}.

Now, if x\geq 0 , then \sqrt{x}\geq 0 so  -3\sqrt{x}\leq 0, and thus f(x)\in \mathbb{R}, which leads us to affirm that the range of  f  is the set of all nonpositive numbers, \{x\in \mathbb{R} : x \leq 0 \}.

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Answer:

The value of a = 5.

the value of b = 6.

Step-by-step explanation:

Given the points on the line

  • (6, 10)
  • (a, 8)
  • (4, b)
  • (2, 2)

Given that all of the points are on the same line and the line represents a linear function.

Thus, the slope between any two points must be the same.

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(x₂, y₂) = (2, 2)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [2 - 10] / [2 - 6]

               = -8 / -4  

               = 2

Thus, the slope of the line = m = 2

Determine the value 'a'

(x₁, y₁) = (6, 10)

(x₂, y₂) = (a, 8)

Using the slope formula to determine the value of 'a'

Slope =  [y₂ - y₁] /  [x₂ - x₁]

As the slope between two points is 2.

now substitute slope = 2, (x₁, y₁) = (6, 10) and (x₂, y₂) = (a, 8) in the slope formula

Slope =  [y₂ - y₁] /  [x₂ - x₁]

2 = [8 - 10] / [a - 6]

2(a - 6) = 8 - 10

2a - 12 = -2

2a = -2 + 12

2a = 10

divide both sides by 2

a = 5

Therefore, the value of a = 5.

Determine the value 'b'

(x₁, y₁) = (2, 2)

(x₂, y₂) = (4, b)

Using the slope formula to determine the value of 'b'

Slope =  [y₂ - y₁] /  [x₂ - x₁]

As the slope between two points is 2.

now substitute slope = 2, (x₁, y₁) = (2, 2) and (x₂, y₂) = (4, b) in the slope formula

Slope =  [y₂ - y₁] /  [x₂ - x₁]

2 = [b - 2] / [4 - 2]

2(4 - 2) = b - 2

8 - 4 =b - 2

4 = b - 2

b = 6

Therefore, the value of b = 6

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