Which functions domain consists of all real numbers except -2?

Mathematics

1 answer:

Eddi Din [679]4 years ago

8 0

Answer:

option (a) f(x)= 1/x+2

Step-by-step explanation:

(a) f(x) = 1/ x+2

To find the restriction for domain , we set the denominator =0 and solve for x

x+2 =0, so x=-2

When x=-2 then denominator becomes 0 that is undefined.

So, domain is all real numbers except -2

(b) f(x)= 2x

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

f(x) = 1/ sqrt(x+2)

if we have square root in the denominator then we set the denominator >0 and solve for x. because square root of negative values are undefined

x+2>0, x>-2

Hence domain is all real numbers that are greater than -2

You might be interested in

What class interval is appropriate for the measurement values reported as 4.1 cm?

jekas [21]

4.1 is a measure to the nearest tenth.

The value preceding it is 4.0 while the value following it is 4.2

The midvalue of 4.0 and 4.1 is 4.05 while the midvalue of 4.1 and 4.2 is 4.15

Therefore, the class interval of a measurement values reported as 4.1 cm is 4.05 to 4.14 cm

4 0

3 years ago

Paul wants a bike that cost $400. If he had saved 60% of this amount, how much had he saved.

enyata [817]

Hey!

To solve this problem, we'll first start by creating an equation.

Our Created Equation :

$\frac{400 x 60}{100}$

Now we'll solve it step by step to find the answer.

So we should begin by multiplying the to portion of our fraction.

400 x 60 = 24,000

Next, we divide our answer by 100, since that is the next step to our equation.

24,000 ÷ 100 = 240

So, our answer is...

Paul has already saved $240.00 of the $400.00 he must pay for a new bike.

Hope this helps!

- Lindsey Frazier ♥

4 0

3 years ago

Check my work Check My Work button is not enabled 1 Item 3 Item 3 10 points Beer bottles are filled so that they contain an aver

Romashka-Z-Leto [24]

Answer: The probability that a random selected bottle will have less than 440 ml of beer is 23.882% (0.23882)

find attached drawing of the area under the normal distribution and readings off the normal distribution table

Step-by-step explanation:

QUESTION: Beer bottles are filled so that they contain an average of 445 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 7 ml. a. What is the probability that a randomly selected bottle will have less than 440 ml of beer

ANSWER:

Taken the given data from the question,

mean = μ = 445 ml

standard deviation = σ = 7 ml

x= 440 ml

One would also need to illustrate the area covered by such a region in a normal distribution curve (Kindly find attached a diagram of this)

FIRST STEP Find the z-score

The distribution is a normal distribution, so the z-score is

z = (x-μ)/σ = (440 - 445)/7 = -0.71 (2 d.p)

SECOND STEP Finding the probability of the z-score from a normal distribution which is equivalent to the the probability we are looking for

Pr(x < 440 ml) = Pr (z < -0.71) = 0.23882 [THIS IS GOTTEN FROM THE STANDARD NORMAL DISTRIBUTION TABLE, kindly find attached a picture illustrating the way the solution is gotten from the table]

The standard normal distribution table takes the probability of areas to the left. Reading the table one should take the the value with -0.7 and the 0.01.

Therefore, the probability of a beer chosen at random to be less than 440 ml is 23.882% (leaving in percentage or 0.23882)