All categories

2 years ago

If f'(x)=2/x and f(sqrt(e))=5, then f(e)=

1 answer:

3 0

$f'(x)=\dfrac2x$
$\implies f(x)=\displaystyle\frac2x\,\mathrm dx=2\ln|x|+C$

$f(\sqrt e)=5\implies 5=2\ln|\sqrt e|+C$
$\implies 5=\dfrac22\ln e+C$
$\implies C=4$
$\implies f(x)=2\ln|x|+4$
$\implies f(e)=2\ln|e|+4=6$

You might be interested in

Bob withdrew money from an ATM, put the receipt in an envelope, and filled in the information in his check register.

lora16 [44]

Answer:It is important to record each transaction so Bob knows how much money is in his account. That prevents being overdrawn. Recording debits and deposits helps with budgeting. It is good to keep receipts in case of any bank errors.

Step-by-step explanation:

5 0

1 year ago

Read 2 more answers

Harry's soccer team plays 2 nonconference games for every 3 games that they play against conference opponents. If y represents t

Sergeeva-Olga [200]

The correct answer is y=2/3x

5 0

2 years ago

Read 2 more answers

The graph of f(x) = StartRoot x EndRoot is reflected across the x-axis and then across the y-axis to create the graph of functio

Anna35 [415]

Answer:

The only value that is in the domains of both functions is 0

The range of g(x) is all values less than or equal to 0

Step-by-step explanation:

As the original function is

$f(x) = \sqrt{x}$

Since, domain is the set of all possible input values that define the function, and range is the set of all possible output values for all possible domain values for which the function is defined.

The domain of $f(x) = \sqrt{x}$ will be [0, ∞)

The range of $f(x) = \sqrt{x}$ will be [0, ∞)

Please check the attached figure a for visualizing the graph of $f(x) = \sqrt{x}$ .

Impact of double transformation:

When the function $f(x) = \sqrt{x}$ is reflected across x-axis, the function becomes $y = -\sqrt{x}$ after first transformation

After the second transformation across y-axis, the function $y = -\sqrt{x}$ becomes $g(x) = -\sqrt{-x}$

For

$g(x) = -\sqrt{-x}$

$-x$ must be equal to or greater than zero for $g(x) = -\sqrt{-x}$ to be defined i.e. -x ≥ 0.

So,

-x ≥ 0 can be written as x≤ 0

So,

The domain of $g(x) = -\sqrt{-x}$ will be (∞, 0]
The range of $g(x) = -\sqrt{-x}$ will be (∞, 0]

Please check the attached figure a for visualizing the graph of $g(x) = -\sqrt{-x}$ .

So, from the above discussion, we can say that

0 is the only that is in the domain of both function.
The range of g(x) is all values less than or equal to 0

So,

Only two statements are true about the functions f(x) and g(x) are true which are:

The only value that is in the domains of both functions is 0

The range of g(x) is all values less than or equal to 0

Keywords: graph, function

Learn more about graph and function from brainly.com/question/11152594

#learnwithBrainly

8 0

1 year ago

Read 2 more answers

What is the value of x in this equation: 4x + 5 = 3x + 4? Solve the equation using the algebra tiles.

Snowcat [4.5K]

Answer:

x = -1

Step-by-step explanation:

4x + 5 = 3x + 4

-5 -5

4x = 3x -1

-3x = -3x

1x = -1

x = -1

4 0

2 years ago

Read 2 more answers

Ariel snowboarded down a mountain that has a vertical height of 1,200 feet. She traveled a distance of 2,400 feet from the top o

KIM [24]

For this case what you should do is use the following trigonometric relationship
senx = (1200) / (2400)
senx = 0.5
Clearing the angle we have
x = ASIN (0.5)
x = 30
Answer:
The angle of elevation from the base to the top of the mountain is 30 °

6 0

2 years ago