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Olenka [21]
3 years ago
14

Given the range of the function find the corresponding domain. f(x)=7x-1 Range {-2,0,4,8}

Mathematics
1 answer:
LenaWriter [7]3 years ago
8 0

f(x) = 7x - 1

-2 = 7x - 1

-2 + 1 = 7x

-1 = 7x

x = -1/7

0 = 7x - 1

1 = 7x

x = 1/7

4 = 7x - 1

4 + 1 = 7x

5 = 7x

x = 5/7

8 = 7x - 1

8 + 1 = 7x

9 = 7x

x = 9/7

So the domain is

Domain = {-1/7, 1/7, 5/7, 9/7}

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Find the perimeter of a field that has length 2/x + 1 and width 5/x^2 -1.
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Answer:

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Step-by-step explanation:

A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle

p=2(l+w)

where

p is the perimeter

l is the length

w is the width

We know from our problem that the field has length 2/x + 1 and width 5/x^2 -1, so l=\frac{2}{x+1} and w=\frac{5}{x^2-1}.

Replacing values:

p=2(l+w)

p=2(\frac{2}{x+1} +\frac{5}{x^2-1})

Notice that the denominator of the second fraction is a difference of squares, so we can factor it using the formula a^2-b^2=(a+b)(a-b) where a is the first term and b is the second term. We can infer that a=x^2 and b=1^2. So, x^2-1=(x+1)(x-1). Replacing that:

p=2(\frac{2}{x+1} +\frac{5}{x^2-1})

p=2(\frac{2}{x+1} +\frac{5}{(x+1)(x-1})

We can see that the common denominator of our fractions is (x+1)(x-1). Now we can simplify our fraction using the common denominator:

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p=\frac{4x+6}{(x+1)(x-1)}

We can conclude that the perimeter of the field is D)4x + 6/(x + 1)(x - 1).

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