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3 years ago

Let \[f(x) = \frac{3x - 7}{x + 1}.\]find the range of $f$. give your answer as an interval.

1 answer:

7 0

Hello :
let : $y= \frac{3x-7}{x+1}$
calculate : x ......x <span>≠ -1
</span> $y(x+1) = 3x-7$
$yx+y =3x-7$
$yx-3x = -y-7$
$x(y-3) = -7-y$
$x = \frac{y+7}{3-y}$
the inverse function is : $g(x) = \frac{x+7}{3-x}$
domain of : g is the range of : f
as an interval : ]-∞: 3 <span>[</span>U ]3;+∞[

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3 years ago

Help, don’t understand this problem.

Mila [183]

Answer:

(2, 3 )

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2 years ago

Read 2 more answers

Find two consecutive whole numbers such that 4/7 of the larger exceeds 1/2 of the smaller by 5

Darina [25.2K]

Answer:

The consecutive numbers are 62 and 63

Step-by-step explanation:

Let the larger number be represented by x and the smaller number by y,

Provided they are consecutive numbers;

$x = y + 1$ --- Equation 1

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$\frac{4x}{7} = \frac{y}{2} + 5$ --- Equation 2

Required

Find x and y

Multiply both sides of equation 2 by 14

$14 * \frac{4x}{7} = 14 * \frac{y}{2} + 14 * 5$

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Substitute y + 1 for x in equation 2

$8(y + 1) = 7y + 70$

Open bracket

$8y + 8 = 7y + 70$

Collect like terms

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3 years ago

The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated

statuscvo [17]

We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.

We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.

So we can define the proportion of coffee that Jeremiah has in his body as:

P(t) = 1*e^{k*t}

Such that:

P(4.8 h) = 0.5 = 1*e^{k*4.8}

Then, if we apply the natural logarithm we get:

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Ln(0.5) = k*4.8

Ln(0.5)/4.8 = k = -0.144

Then the equation is:

P(t) = 1*e^{-0.144*t}

Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:

P(t) = 0.6 = 1*e^{-0.144*t}

Again, we use the natural logarithm:

Ln(0.6) = Ln(e^{-0.144*t})

Ln(0.6) = -0.144*t

Ln(0.6)/-0.144 = t = 3.55

So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.

If you want to learn more, you can read:

brainly.com/question/19599469

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2 years ago