All categories

2 years ago

What is the inverse of f(x)=x^4+7 for x>0 where function g is the inverse of function f? -

Mathematics

1 answer:

Ann [662]2 years ago

7 0

Answer:

$g(x) = \sqrt[4]{x-7},~ x\geq 7$

Step by step explanation:

$y= f(x) = x^4+7\\\\\text{Replace x with y and solve for y:}\\\\~~~~~~~x = y^4 +7\\\\\implies y^4 = x-7\\\\\implies y = \pm\sqrt[4]{x-7}\\\\ \implies f^{-1}(x) = \pm\sqrt[4]{x-7}$

You might be interested in

Simplify so that there are only positive exponents (3^9/3^-5)

fomenos

Answer:

3^14

Step-by-step explanation:

(3^9/3^-5)

We know that when we have a^b / a^c = a^(b-c)

3^(9 - -5)

3^(9+5)

3^14

5 0

3 years ago

Questions 1,2, and 3 please. These are the last questions in the packet and I'm sorta stuck on them. Could anyone help explain h

Delicious77 [7]

Where are the questions?

4 0

4 years ago

Calculs from the north you walk 1 mile and a temperature was 5 degrees from the west you walk 1 mile and the temperature change

MakcuM [25]

Answer: 6.4 degrees

Step-by-step explanation:

a= 5 degrees temperature difference to the north gives the opposite of the triangle,

b = 4 degrees temperature difference to the west gives the adjacent,

c = temperature difference of 1 mile to the south east gives the hypotenuse.

Therefore,

Using Pythagoras equation,

c² = b² + a²

c = sqrt( 5² + 4²)

c = sqrt(41) = 6.4 degrees

Therefore, there will be 6.4 degrees temperature difference 1 mile to the south east

4 0

3 years ago

Nicole wants to replace a glass window in her restaurant. The window is in the shape of a square. It’s side lengths are 11 feet.

Ede4ka [16]

Answer:

275

Step-by-step explanation:

6 0

3 years ago

The health of the bear population in a park is monitored by periodic measurements taken from anesthetized bears. A sample of the

Vikki [24]

Answer:

$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

Step-by-step explanation:

Assuming the following dataset:

77, 349,417,349, 167 , 225, 265, 360,205

145,335,40,139, 177,108, 163, 202, 22

123,439, 125,135, 86,43, 217,49, 156

119,178, 151, 61, 350, 312, 91, 89,89

We can calculate the sample mean with the followinf formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}= 182.167$

And the sample deviation with:

$s = \sqrt{\frac{\sum_{i=1}^n (X_i-\bar X)^2}{n-1}}=114.05$

The sample size on this case is n =36.

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=182.167$ represent the sample mean

$\mu$ population mean (variable of interest)

s=114.05 represent the sample standard deviation

n=36 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The point estimate of the population mean is $\hat \mu = \bar X =182.167$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=36-1=35$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,35)".And we see that $t_{\alpha/2}=2.03$

Now we have everything in order to replace into formula (1):

$182.167-2.03\frac{114.05}{\sqrt{36}}=143.580$

$182.167+2.03\frac{114.05}{\sqrt{36}}=220.754$

So on this case the 95% confidence interval would be given by (143.580;220.754)

5 0

3 years ago