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Mathematics

1 answer:

Sloan [31]3 years ago

7 0

Answer:

a) 2x+2x+x+x+x=42

b) x=6

c) 6 cm, 6cm, 6cm, 12cm, 12cm

Step-by-step explanation:

First think of how you'll get perimeter. Since in the question it says you add all of the sides to get the perimeter, you write the variables being added together and equal it to 42. Next, you add all of the x's together, which you would get 7x=42. Then, you divide 7x and 42 by 7, giving you x=6. Finally, you plug in 6 into the x's, making sure to multiply the ones that are 2(6) into 12. To check if this is true, add the sides together and make sure you get 42.

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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>

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Explanation:

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

f(x) = 3x+2

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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.

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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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