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3 years ago

Can anyone help me please

Mathematics

1 answer:

denis23 [38]3 years ago

6 0

Im pretty sure that it is D or the last one. If you're equally sharing something, you would have to divide it.

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(a) Find the domain off (x) = ln(ex − 3).<br> (b) Find F −1 and its domain.

Anettt [7]

Answer:

a) The domain of f(x) is $x > 1.1$ .

The inverse function is:

$y = \ln{(e^{x} + 3)}The domain is all the real values of x.Step-by-step explanation:(a) Find the domain off f(x) = ln(e^x − 3)The domain of f(x) = ln(g(x)) is g(x) > 0. That means that the ln function only exists for positive values.So, here we have[tex]g(x) = e^{x} - 3$

So we need

$e^{x} - 3 > 0$

$e^{x} > 3$

Applying ln to both sides

$\ln{e^{x}} > \ln{3}$

$x > 1.1$

So the domain of f(x) is $x > 1.1$ .

(b) Find F −1 and its domain.

$F^{-1}$ is the inverse function of f.

How do we find the inverse function?

To find the inverse equation, we change y with x to form the new equation, and then we isolate y in the new equation. So:

Original equation:

f(x) = y = \ln{e^{x} - 3}

New equation

$x = \ln{e^{y} - 3}$

Here, we apply the exponential to both sides:

$e^{x} = e^{\ln{e^{y} - 3}}$

$e^{y} - 3 = e^{x}$

$e^{y} = e^{x} + 3$

Applying ln to both sides

$\ln{e^{y}} = \ln{e^{x} + 3}$

The inverse function is:

$y = \ln{e^{x} + 3}$

The domain is

$e^{x} + 3 > 0$

$e^{x} > -3$

$e^{x}$ is always a positive number, so it is always going to be larger than -3 no matter the value of x. So the domain are all the real values.

5 0

3 years ago

I need help on this question

My name is Ann [436]

If the weight of wrestlers on the team varies by 74 pounds, the best way to measure this would be the range.

The range indicates how much difference there is between the maximum and the minimum values, thus making it perfectly suited for finding the variance between the weights of wrestlers.

The most popular M&M color being green could be best verified by the mode.

The mode of a set is the most commonly occurring number in that set, so this would be the best way to find the most commonly occurring type of candy.

If the mean price for a download is $1.96, this could be verified by finding the mean.

The mean is the average of a data set, so this could verify that this price was the best indication of the average of the mp3 downloads.

Finally, if half the students in PE are 15 or older, this could be determined by the median.

The median is the middlemost value in a data set, so it would help you in this instance because it would allow you to see where the halfway point was in the ages of PE participants.

Hope this helps!

3 0

3 years ago

Pls help<br> Pls help <br> Pls gelp

weqwewe [10]

Answer:

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Which is the equation of a line that is parallel to the line represented by y= 7/6 x + 4 ?

Nesterboy [21]