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motikmotik
3 years ago
5

Martin likes to make flower bouquets that have 3 daffodils and 4 tulips per vase. A daffodil has a mass of d grams, a tulip has

a mass of ttt grams, and the vase has a mass of v grams.
The expression 5(3d+4t+v)5(3d+4t+v)5, left parenthesis, 3, d, plus, 4, t, plus, v, right parenthesis describes the mass of 5 bouquets.
Match each amount in the situation with the expression that represents it.
Mathematics
1 answer:
Elza [17]3 years ago
8 0

Answer:this is the order of the things to put them

number of bouquets: 5

mass of bouquets: 3d+4t+v

mass of the tulips in one bouquet: 4t

mass of the daffodils in one bouquet: 3d

Step-by-step explanation:

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The function of f(x) = 3x + 2 has a domain of -3 < x < 5. What is the domain of f-1(x)?
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<h3>Answer:    -7 < x < 17</h3>

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

Explanation:

Plug in the lower bound of the domain, which is x = -3

f(x) = 3x+2

f(-3) = 3(-3)+2

f(-3) = -9+2

f(-3) = -7

If x = -3, then the output is y = -7. Since f(x) is an increasing function (due to the positive slope), we know that y = -7 is the lower bound of the range.

If you plugged in x = 5, you should find that f(5) = 17 making this the upper bound of the range.

The range of f(x) is -7 < y < 17

Recall that the domain and range swap places when going from the original function f(x) to the inverse f^{-1}(x)

This swap happens because how x and y change places when determining the inverse itself. In other words, you go from y = 3x+2 to x = 3y+2. Solving for y gets us y = (x-2)/3 which is the inverse.

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

In short, we found the range of f(x) is -7 < y < 17.

That means the domain of the inverse is -7 < x < 17 since the domain and range swap roles when going from original to inverse.

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