Help I need this answer before the day is over

Marizza181 [45]

Answer:

A. y = (x - 12)/3

B. See below

C. -2

Step-by-step explanation:

In general, to find the inverse of an equation like this, all you have to do is swap the x and y variables then solve for y.

First, replace "f(x)" with y... y = 3x + 12

Next, swap x and y... x = 3y + 12

Now, solve for y. You should get y = (x - 12)/3, and this is the inverse of f(x) = 3x + 12. Since the inverse is a different equation, you can rename "y" to be "g(x)" to help with part B.

Composite functions just mean you take one and plug it into the other. With inverses, plugging the functions into one another should return just x. In this case, you can take g(x) and plug it into f(x); so you can find f(g(x)).

Replace every instance of x with g(x). f(g(x) looks kind of weird, but it functions the same as every other function; you just plug something in and get something out.

f(g(x)) = 3[(x - 12)/3] + 12

Simplify; cancel out the 3s, add 12 and -12. What's left? x. This is how you know these two functions are inverses of one another. To help yourself visualize, plug them into a graphing calculator and see what inverses like compared to one another so you can understand how they behave graphically!

For part C, all you have to do is plug -2 into g(x) first, then plug the result of that into f(x). Try it on your own. g(-2) should give you -14/3, and when you plug that into f(x), you should end up with -2.

For the domain, you should recognize that both the inverse and the original function are linear. There are no square root symbols, logarithms, or variables in the denominators that would limit the domain (i.e. when you have x - 3 as the denominator, so you know you can't plug in 3 because it will give you 0 and you can't divide by zero). Since there's nothing to mess up the domain, it's all real numbers.

8 0

3 years ago

Pls help. i will give brainliest

fenix001 [56]

Answer:

247 = j - 285

Step-by-step explanation:

Anything that is labeled with "is" will be what the entire equation is equal to. (Also because the instructions are asking for an equation which is equal to something). Also, fewer than is the subtraction of two things. In this case it will be 285 and j. In the end the equation will be:

247 = j - 285

Hope this helped.

7 0

3 years ago

Share £56 in the ratio 3:4

vagabundo [1.1K]

Answer:

£24 : £32

Step-by-step explanation:

Add the parts of the ratio 3 + 4 = 7

Divide the amount by 7 to find the value of one part

£56 ÷ 7 = £8 ← one part of the ratio

3 parts = 3 × £8 = £24

4 parts = 4 × £8 = £32

8 0

3 years ago

Cos Ф<0 and tan Ф >0 <br> Determine the quadrant that the terminal side of Ф lies

rodikova [14]

3rd quadrant. Below is a picture that explains what is positive and in what quadrant. I use the term <em>All students take calculus</em>. If you start in the 1st and go through 2nd, 3rd and forth:

A in all stands for All positive
S in students stands for sin and its inverse (csc) is positive.
T in take stands for tan and its inverse (cot) is positive.
C in calculus stands for cos and its inverse (sec) is positive.

3 0

4 years ago

Read 2 more answers

ASK YOUR TEACHER An article reported that for a sample of 42 kitchens with gas cooking appliances monitored during a one-week pe

xxMikexx [17]

Answer:

$654.16-2.02\frac{165.23}{\sqrt{42}}=602.66$

$654.16+2.02\frac{165.23}{\sqrt{42}}=705.66$

So on this case the 95% confidence interval would be given by (602.66;705.66)

Step-by-step explanation:

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".

$\bar X=654.16$ represent the sample mean

$\mu$ population mean (variable of interest)

s=165.23 represent the sample standard deviation

n=42 represent the sample size

Solution to the problem

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

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

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

$df=n-1=42-1=41$

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(0.025,41)".And we see that $t_{\alpha/2}=2.02$

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

$654.16-2.02\frac{165.23}{\sqrt{42}}=602.66$

$654.16+2.02\frac{165.23}{\sqrt{42}}=705.66$

So on this case the 95% confidence interval would be given by (602.66;705.66)

7 0

4 years ago