Mathematics High School

Match each function with its inverse function. Use function composition to determine your answers.
Please help

Answers

Answer 1

Answer:

For f(x) = x^2 - 2x + 1, the inverse is g(x) = √x + 1

For f(x) = 2 - 5*x the inverse is g(x) = (2 - x)/5

For f(x) = 5*(x - 2) the inverse is g(x) = x*(1/5) + 2

for f(x) = (x - 2)^2 - 1 the inverse is g(x) = √(x + 1) + 2

Step-by-step explanation:

If we have two functions f(x) and g(x) such that these functions are inverse, then we have:

f( g(x)) = x

and

g( f(x)) = x

Let's start with the function:

f(x) = x^2 - 2x + 1

Notice that we can rewrite this as:

f(x) = x^2 - 2*x + 1 = (x - 1)^2

Because this is a quadratic function, the inverse function needs to have a square root, then the inverse function can be the third or fourth one.

Let's try with the last one:

g(x) = √x + 1

Then:

f( g(x)) = ( √x + 1 - 1)^2 = (√x )^2 = x

g( f(x)) = √(x - 1)^2 + 1 = (x - 1) + 1 = x

Then for the function:

f(x) = x^2 - 2x + 1, the inverse is: g(x) = √x + 1

Now let's find the inverse for the second function:

f(x) = 2 - 5*x

The inverse of this function will be also a linear function, and the slope of the inverse will be the inverse of this slope, then the inverse may be the first or second options.

Let's try with:

g(x) = (1/5)*x - 2

Then:

f( g(x) ) = 2 - 5*((1/5)*x - 2) = 2 - x + 10

Then this g(x) is not the inverse of the function.

Let's try with g(x) = (2 - x)/5

Then:

f( g(x)) = 2 - 5*(2 - x)/5 = 2 - 2 + x = x

g( f(x)) = (2 - 2 - 5*x)/5 = 5*x/5 = x

For the function f(x) = 5*(x - 2)

The inverse should be the remaining linear function:

g(x) = x*(1/5) + 2

Then:

f( g(x)) = 5*(x*(1/5) + 2 - 2) = 5*x*(1/5) = x

g( f(x)) = (5*(x - 2) )*(1/5) + 2 = (x - 2) +2 = x

For the last function, f(x) = (x - 2)^2 - 1

The inverse function will be:

g(x) = √(x + 1) + 2

The compositions are:

f( g(x)) = (√(x + 1) + 2 - 2)^2 - 1 = (√(x + 1))^2 - 1 = (x + 1) - 1 = x

g(f(x)) = √((x - 2)^2 - 1 + 1) + 2 = √((x - 2)^2 + 2 = x

Answer 2

Answer:

PLATO ANSWER

Step-by-step explanation:

Related Questions

Hi there! please please help:)) have a good day

Answers

Answer:

Step-by-step explanation:

sorry if wrong dont report

Answer:

can barely read the graph luv :(

A phone company charges a sign-up fee of $3.50, plus $x for every hour the phone is
used. If Brian talked on the phone for 12 hours and paid a total of $75.50, which of the
following equations can be used to find, x, the hourly rate of the phone plan?

Answers

Answer:

...........................

Which point is an outlier?
A. (0.1, 575)
B. (0.4, 400)
C. (0.99, 2, 190)
D. There is no outlier

Answers

Answer:

190 is the outlier

Step-by-step explanation:

i believe that c is the outlier

Please help me? I am confused.

Answers

ANSWER: A. x=4

Explanation: 7-2x=2x(x-4)-1

7-2x=2x-9

-2x-2x=-9-7

-4x=-16

which will get you your answer x=4

A person in the audience of a reality show has a 16% chance of winning free movie tickets. What is the chance that a person in the audience does not win free movie tickets?
32%
34%
72%
84%

Answers

Answer: 84%

Step-by-step explanation: divide 16 by 100

Solve for x.
(x - 12)
2x
51

Answers

Answer:

114

Step-by-step explanation:

144 is the answer I think

find the arc length

Answers

Answer:

9.77 units

Step-by-step explanation:

full circle circumference = 2rπ = 2(16)(3.14) = 100.48

(35°/360°)(100.48) = 9.77 units

Can someone pleaseeee help and if you’re correct i’ll give brainliest

Answers

Answer:

can you copy and paste it on a question its kinda blurry for me

Step-by-step explanation:

Answer:

B / The Girl

Step-by-step explanation:

Suppose the circumference of a circle is 6 pi. What is its diameter?

Answers

Answer:

the ans is 12

Step-by-step explanation:

C= RadiusxPi

Radius=6

D=Rx2

D=12

(hope this helps can i plz have brainlist :D hehe)

Is this a function? Why or why not?

Answers

Answer:

Yes because there are no repeated dependent variables.

Step-by-step explanation:

I need this done thanks!

Answers

Step-by-step explanation:

Median= n+1/2 ( if n is even )

So,

10+1/2=11/2=5.5

Therefore,

135 is your second answer

Spread of the data = in the above mentioned picture the wave given to find the spread of the data

Hope it helps

it's all on the picture

Answers

Answer:

y = 54

Step-by-step explanation:

45 = y - 9

+9 +9

54 = y

y= 54

A bicyde store costs $2400 per month to operate. The store pays an average of 570 per bike. The average selling price of each bicyde is $100. How many bicydes must the store soil each month to break even?
The store must sel bicycles each month to break even.
(Type a whole number)

Answers

Answer:

It can't buy a bike for 570 and sell it fo 100. They'll just be losing money on top of rent

Step-by-step explanation:

how many distinguishable permutation are possible with all the letters of the word sequence

Answers

Step-by-step explanation:

hey, hope this helps/ is right :))

Given tan⁡ θ = 7/24, and ⁡θ terminates in Quadrant III, determine the value of cos⁡ θ.

Answers

Answer:

-24/25

Step-by-step explanation:

Because it is in quadrant 3, cosine is negative. Hypotenuse=25, Adj=-24, Opp, -7. Cos=Adj/Hyp. -24/25

It is Given that tan⁡ θ = 7/24, and ⁡θ terminates in Quadrant III, Thus the value of cos⁡ θ is -24/25.

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

Given tan⁡ θ = 7/24, and ⁡θ terminates in Quadrant III,

we want to determine the value of cos⁡ θ.

Because it is in quadrant 3, cosine is negative.

Hypotenuse = 25, Adjcent = -24, Opposite = -7.

Cos θ = Adjcent /Hypotenuse .

= -24/25

Learn more about trigonometry;

https://brainly.com/question/14746686

#SPJ2

someone help me with this plss

Answers

Answer:

C. b=1053

Step-by-step explanation:

Isolate b:

0.25b+168.75=432Subtract 168, 0.25b=263.25Divide by 0.25, b=1053

Answer:

C) b = 1053

Step-by-step explanation:

.25b = 263.25

b = 263.25/0.25

b = 1,053

Write an equivelant expression using distributive property for these two inequalities
8(−x−12)

5. −8(−x−34y + 72)

Answers

Step-by-step explanation:

[tex]8( - x - 12) \\ - 8x - 12 \\ \\ \\ - 8( - x - 34y + 72) \\ 8x + 272y + 576[/tex]

I hope that is useful for you :)

What phrase describes slope?

A Constant rate of change

B constant rate of percent

C constant rate of interest

Answers

Answer:

-A Constant rate of change

Step-by-step explanation:

I learned this for years.

Graph the function y = 6 – 2x. Click the intercepts to show the coordinates.

Answers

Answer:

Step-by-step explanation:

Let's find and use the intercepts. They speed up graphing of lines.

y-intercept: In y = 6 – 2x, let x = 0. Then y = 6, and the y-intercept is (0, 6).

x-intercept: In y = 6 – 2x, let y = 0. Then 2x = 6, and x = 3. The x-intercept is therefore (3, 0).

Plot these two points and then draw a line through both.

I need help! It is confusing, I need a little help

Answers

The answer is 312cm hope this helped

65/p • 3 when p = 5

Answers

Answer:

Step-by-step explanation:

65/5=13

13x3=39

Answer:

Step-by-step explanation:

Note that p = 5. Plug in 5 for p in the expression. Remember to follow the

left-> right rule:

65/p • 3

65/5 • 3

(65/5) • 3

(13) • 3 = 39

39 is your answer.

Paolo keeps track of his favorite baseball player's batting average, and notices the average is 0.4727272.... If his player has 55 at bats, what is the number of hits?

Answers

Answer:

No of hits = 26

Step-by-step explanation:

Given that,

Batting average = 0.4727272

His player has 55 at bats.

We need to find the number of hits. Let the number of hits be x. Using formula for average as :

[tex]\dfrac{x}{55}=0.4727272\\\\x=0.4727272\times 55\\\\x=25.99\\\\or\\\\x=26[/tex]

So, there are 26 number of hits.

!! PLEASE HELP !!
What is the domain of f(x)=(1/2)x?

Answers

Answer:

D: {-∞ < x < 0}

Step-by-step explanation:

Diane 4 1/3 cut feet of tape. How much is this in inches?

Answers

Answer:

52 inches

Step-by-step explanation:

Answer:

52 imches

Step-by-step explanation:

each foot is 12 inches

12x4=48

12/3=4

this is the 1/3 feet

add 48 and 4 and you get 52

what is y=-x-4 if x=-2

Answers

Answer:

-2

Step-by-step explanation:

The answer is -2

Explanation:

First of all we need to identify the problem.

Y= -X-4

We can tell already from this that the X is going to be negative.

If X=-2

Now we can change the problem to:

Y= -2-4

And can even change it to

-2-4

Well the way I learned it

A negative number minus a negative number is a negative number

A positive number minus a positive number is a positive number

Simple Right?

So what's a negative number minus a positive number?

Its a negative number!

So the answer is -6

Vincent has a box of popsicles. There are 12 cherry, grape 10 orange, and 6 blue raspberry If he reaches in the box and pulls one out at random, what the probability it will be blue raspberry?

Answers

Answer:

6:28 or 3:14

Step-by-step explanation:

if you add all the flavor amounts up, which is 12 + 10 + 6, you get 28. 6 of those 28 popsicles are blue raspberry, so the ratio is 6:28. if it needs to be simplified, its 3:14 because 6/2 is 3 and 28/2 is 14

Answer:

6:28 if you add all Popsicles it gives you 28,so the probability that he will pick raspberry are 6 ,so if you simplyfy further its 3:14

Please help me. I don’t understand matrices

Answers

Answer:

A. [tex]\orange {\begin{bmatrix} 4 & 11 \\ 3 & 0 \end{bmatrix}} [/tex]

Step-by-step explanation:

[tex] A= \begin{bmatrix} 5 & - 8 \\ 3 & 0\end{bmatrix} \: and \: B= \begin{bmatrix} 2 & - 9 \\ 1 & 0\end{bmatrix} [/tex]

[tex]\therefore 2A= 2\begin{bmatrix} 5 & - 8 \\ 3 & 0\end{bmatrix} \: and \: \: 3B= 3\begin{bmatrix} 2 & - 9 \\ 1 & 0\end{bmatrix} [/tex]

[tex]\therefore 2A= \begin{bmatrix} 10 & - 16 \\ 6 & 0 \end{bmatrix} \: and \: \: 3B= \begin{bmatrix} 6 & - 27 \\ 3 & 0\end{bmatrix} [/tex]

[tex]\therefore 2A-3B= \begin{bmatrix} 10 & - 16 \\ 6 & 0 \end{bmatrix} - \begin{bmatrix} 6 & - 27 \\ 3 & 0 \end{bmatrix} [/tex]

[tex]\therefore 2A-3B= \begin{bmatrix} 10-6 & - 16-(-27) \\ 6-3 & 0-0 \end{bmatrix} [/tex]

[tex]\therefore 2A-3B= \begin{bmatrix} 4 & - 16+27 \\ 3 & 0 \end{bmatrix} [/tex]

[tex]\huge \red {\therefore 2A-3B= \begin{bmatrix} 4 & 11 \\ 3 & 0 \end{bmatrix}} [/tex]

Can u help me guys this is hard

Answers

25% as a fraction is 1/4 and as a decimal it’s 0.25
1/2 as a percentage is 25% and as a decimal it’s 0.25
6.66% as a fraction is 333/50 and as a percentage it’s 666%

PLEASE HELP!!!

The heights of the children at a summer camp are normally distributed with a mean of 54 inches and a standard deviation of 2.4 inches

What is the height of a child with a -score of 1.5?

Answers

Answer:

he is around 4 ft 5 ish

Step-by-step explanation:

yeah

Erik states that the two cones below have the same volume because of Cavalieri’s principle. 2 cones are shown. The first cone has a radius of r, a slant length of c, and a height of b. The second cone has a radius of r, a height of a, and a slant length of b. Is Erik’s statement correct? Why or why not? Yes, the solids are both cones and appear to have the same volumes. Yes, the area of the bases and the heights of the cones are the same, so the volumes are equal. No, the heights of the cones are not the same, so Cavalieri’s principle does not apply.

Answers

Answer:

D. No, the heights of the cones are not the same, so Cavalieri’s principle does not apply.

Step-by-step explanation:

Correct on Edge.

Answer:

The person above me is correct but the option is C.

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Match each function with its inverse function. Use function composition to determine your answers. Please help

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Match each function with its inverse function. Use function composition to determine your answers.
Please help