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3 years ago

Select the correct answer What is the inverse of the function f(x)=x+1/x

Mathematics

2 answers:

expeople1 [14]3 years ago

8 0

Answer:

Option B is the correct option.

Step-by-step explanation:

Let y = f ( x )

$y = \frac{x + 1}{x}$

Apply cross product property

$xy = x + 1$

Move 'x' to L.H.S and change it's sign

$xy - x = 1$

Take x as common

$x(y - 1) = 1$

$x = \frac{1}{y - 1}$

Replace x by f ⁻¹(x) and y by x

${f}^{ - 1} (x) = \frac{1}{x - 1}$

Hence, Option B is the correct option.

Hope this helps..

Best regards!!

Sedaia [141]3 years ago

7 0

Answer:

$\boxed{\mathrm{B}}$

Step-by-step explanation:

$f(x)=\frac{x+1}{x}$

$y=\frac{x+1}{x}$

Make x as subject.

Multiply both sides by x.

$yx=x+1$

Subtract both sides by x.

$yx-x=1$

Factor out x.

$x(y-1)=1$

Divide both sides by y-1.

$x=\frac{1}{y-1}$

Switch variables.

$y=\frac{1}{x-1}$

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The Venn diagram shows event A and event B comprised of outcomes from the same sample space. The probability of event A is given

Masteriza [31]

Answer:

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1

A=45

Step-by-step explanation:

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3 years ago

4) Arnold ate breakfast at a restaurant. His total came to $76.75. There is an 8% sales tax and 15% tip. What is Arnold's total

lisov135 [29]

Answer:

The total cost is $95.32.

Step-by-step explanation:

Given:

Total came to $76.75. There is an 8% sales tax and 15% tip.

Now, to find the total cost.

8% sales tax is there so we calculate the amount after adding sales tax:

$76.75 + 8% of $76.75

$76.75+\frac{8}{100}\times 76.75$

$76.75+0.08\times 76.75$

$76.75+6.14$

$82.89$

The cost after sales tax is $82.89.

Now, the cost after 15% tip:

$82.89 + 15% of $82.89

$82.89+\frac{15}{100}\times 82.89$

$82.89+0.15\times 82.89$

$82.89+12.43$

$95.32$

The cost after the tip is $95.32.

Therefore, the total cost is $95.32.

8 0

3 years ago

A limnologist wishes to estimate the mean phosphate content per unit volume of lake water. It is knownfrom studies in previous y

telo118 [61]

Answer: 68

Step-by-step explanation:

As per given , we have

Population standard deviation : $\sigma=4$

Critical value for 90% confidence interval = $z_{\alpha/2}=1.645$

Margin of error : E= 0.8 milligrams

The formula to find the sample size is given by :-

$n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2$

i.e. $n=(\dfrac{(1.645)(4)}{0.8})^2=(8.225)^2$

$=67.650625\approx68$

Hence, the limnologist must analyze 68 samples.

6 0

3 years ago

A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16. (G

dezoksy [38]

Answer:

a) The mean of a sampling distribution of $\\ \overline{x}$ is $\\ \mu_{\overline{x}} = \mu = 20$ . The standard deviation is $\\ \frac{\sigma}{\sqrt{n}} = \frac{16}{\sqrt{64}}=2$ .

b) The standard normal z-score corresponding to a value of $\\ \overline{x} = 16$ is $\\ Z = -2$ .

c) The standard normal z-score corresponding to a value of $\\ \overline{x} = 23$ is $\\ Z = 1.5$ .

d) The probability $\\ P(\overline{x}$ .

e) The probability $\\ P(\overline{x}>23) = 1 - P(Z$ .

f) $\\ P(16 < \overline{x} < 23) = P(-2 < Z < 1.5) = P(Z$ .

Step-by-step explanation:

We are dealing here with the concept of a sampling distribution, that is, the distribution of the sample means $\\ \overline{x}$ .

We know that for this kind of distribution we need, at least, that the sample size must be $\\ n \geq 30$ observations, to establish that:

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

In words, the distribution of the sample means follows, approximately, a normal distribution with mean, $\mu$ , and standard deviation (called standard error), $\\ \frac{\sigma}{\sqrt{n}}$ .

The number of observations is n = 64.

We need also to remember that the random variable Z follows a standard normal distribution with $\\ \mu = 0$ and $\\ \sigma = 1$ .

$\\ Z \sim N(0, 1)$

The variable Z is

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [1]

With all this information, we can solve the questions.

Part a

The mean of a sampling distribution of $\\ \overline{x}$ is the population mean $\\ \mu = 20$ or $\\ \mu_{\overline{x}} = \mu = 20$ .

The standard deviation is the population standard deviation $\\ \sigma = 16$ divided by the root square of n, that is, the number of observations of the sample. Thus, $\\ \frac{\sigma}{\sqrt{n}} = \frac{16}{\sqrt{64}}=2$ .

Part b

We are dealing here with a random sample. The z-score for the sampling distribution of $\\ \overline{x}$ is given by [1]. Then

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{16 - 20}{\frac{16}{\sqrt{64}}}$

$\\ Z = \frac{-4}{\frac{16}{8}}$

$\\ Z = \frac{-4}{2}$

$\\ Z = -2$

Then, the standard normal z-score corresponding to a value of $\\ \overline{x} = 16$ is $\\ Z = -2$ .

Part c

We can follow the same procedure as before. Then

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{23 - 20}{\frac{16}{\sqrt{64}}}$

$\\ Z = \frac{3}{\frac{16}{8}}$

$\\ Z = \frac{3}{2}$

$\\ Z = 1.5$

As a result, the standard normal z-score corresponding to a value of $\\ \overline{x} = 23$ is $\\ Z = 1.5$ .

Part d

Since we know from [1] that the random variable follows a standard normal distribution, we can consult the cumulative standard normal table for the corresponding $\\ \overline{x}$ already calculated. This table is available in Statistics textbooks and on the Internet. We can also use statistical packages and even spreadsheets or calculators to find this probability.

The corresponding value is Z = -2, that is, it is two standard units below the mean (because of the negative value). Then, consulting the mentioned table, the corresponding cumulative probability for Z = -2 is $\\ P(Z$ .

Therefore, the probability $\\ P(\overline{x}$ .

Part e

We can follow a similar way than the previous step.

$\\ P(\overline{x} > 23) = P(Z > 1.5)$

For $\\ P(Z > 1.5)$ using the cumulative standard normal table, we can find this probability knowing that

$\\ P(Z1.5) = 1$

$\\ P(Z>1.5) = 1 - P(Z$

Thus

$\\ P(Z>1.5) = 1 - 0.9332$

$\\ P(Z>1.5) = 0.0668$

Therefore, the probability $\\ P(\overline{x}>23) = 1 - P(Z$ .

Part f

This probability is $\\ P(\overline{x} > 16)$ and $\\ P(\overline{x} < 23)$ .

For finding this, we need to subtract the cumulative probabilities for $\\ P(\overline{x} < 16)$ and $\\ P(\overline{x} < 23)$

Using the previous standardized values for them, we have from Part d:

$\\ P(\overline{x}$

We know from Part e that

$\\ P(\overline{x} > 23) = P(Z>1.5) = 1 - P(Z$

$\\ P(\overline{x} < 23) = P(Z1.5)$

$\\ P(\overline{x} < 23) = P(Z$

Therefore, $\\ P(16 < \overline{x} < 23) = P(-2 < Z < 1.5) = P(Z$ .

5 0

3 years ago

In circle A shown below, BD with a line above is the diameter and the measure of arc CB is 54 degrees. What is the measure of an

Vinil7 [7]

The complete question in the attached figure

we know that
the triangle ACB is an isosceles triangle
AC=AB----------> equals to the radius
so
∡ACB=∡CBA
the angle ∡CAB is equals to 54° by central angle
so
180°=54°+2*∡CBA--------> ∡CBA=[180-54]/2-----> 63°
∡CBA=63°
∡DBC=∡CBA-----------> ∡DBC=63°

the answer is
∡DBC=63°

6 0

3 years ago

Read 2 more answers