Show algebraically that f and g are inverse functions:
g = sqrt(x+8)-4
f=x^2+8x+8

Answers

Answer 1

Answer:

See Below.

Step-by-step explanation:

By definition, if two functions, f and g, are inverses, then:

[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]

We are given the two functions:

[tex]\displaystyle g(x) = \sqrt{x + 8} -4 \text{ and } f(x) = x^2 + 8x + 8[/tex]

Find f(g(x)) and g(f(x)):

[tex]\displaystyle \begin{aligned} f(g(x)) &= (\sqrt{x + 8} -4)^2 + 8(\sqrt{ x+ 8}-4) + 8 \\ \\ &= ((x+8) -8\sqrt{x + 8} +16) + 8\sqrt{x + 8} - 32 + 8 \\ \\ &= x + (-8\sqrt{x+8} + 8\sqrt{x + 8}) +(16 - 32 + 8 + 8) \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}[/tex]

And:

[tex]\displaystyle \begin{aligned}g(f(x)) &= \sqrt{(x^2 + 8x + 8) + 8} - 4 \\ \\ &= \sqrt{x^2 + 8x+16 } - 4 \\ \\ &=\sqrt{(x+ 4)^2} - 4 \\ \\ &= (x +4) - 4 \\ \\ &= x \stackrel{\checkmark}{=} x \end{aligned}[/tex]

Hence, f and g are indeed inverses of each other.


Related Questions

Which number is a whole number but not a
natural number?
0
5
1

Answers

0 because natural numbers are positive

5. a) Write the smallest and largest number of 6 digits.

Answers

Answer:

smallest:100000, and largest:999999

Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate

Answers

Answer:

26.13

Step-by-step explanation:

to find the area of a circle, it's pi*r squared:

pi*3squared=9pi

it's a semi-circle so you divide it by two=4.5pi

they are telling us to use 3.14 instead of pi, so it would be:

4.5*3.14=14.13

now we find the area of the triangle. And we use the formula, (height*base)/2:

6*4/2=12

now we add the sums together, which is:

12+14.13=26.13

the area of a rectangle hall is the same as the area of a square field of side 56 m. if the lenght of hall is 112m. find its breadth​

Answers

Step-by-step explanation:

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ILL DO BRAINLIEST
In the​ diagram, bisects FGI.
Angle FGI is formed from angles FGH and HGI. Angle FGH measures 5 x minus 2 degrees. Angle HGI measures 6 x minus 8 degrees.
a.
Solve for x and find mFGH.
b.
Find mHGI.
c.
Find mFGI.

Answers

Answer:

a. X=6°

b. 6(6)-8= 28°

c. 28+( 5(6)-2) = 56°

For what value(s) of k is the trinomial x² + kx - 24 factorable?

Answers

Answer:

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

ASAP!! NEED HELP! 10 POINTS

Answers

I’m not sure is it correct? Just like I think so

Solve the inequality and graph the solution on the line provided.
7 + 5x < 42

Answers

Answer:

x < 7

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

5x+7<42

Step 2: Subtract 7 from both sides.

5x+7−7<42−7

5x<35

Step 3: Divide both sides by 5.

x<7

For the graph, draw an open circle at 7 and an arrow pointing left.

Hope this helps! :D

Step-by-step explanation:

5x<42-7

5x<35

5x/5<35/5

x<7

FILL IN THE BLANKS


An image has been attached to this question. Fill in the blanks, please make your answer CLEAR and READABLE. Please do not hand in sloppy answers, they will be rated a 1-star. If you don't know what to do, please ask me and I'll do a quick explanation as we need answers in 2 hours. Thank you to those who helped.

Answers

Answer:

Woah you're sounding like a teacher, calm down.

Anyways let's answer this...

Step-by-step explanation:

It's going to be in the order:

Decimal, fraction, percentage.

0.2, 1/5, 20%

0.8, 4/5, 80%

0.5, 1/2, 50%

0.75, 3/4, 75%

0.3, 3/10, 30%

0.6, 3/5, 60%

You see the correlation?

If u want me to explain, hmu

hope this helps :)

a.
Use the domain and range of each of the following relations to determine which is a function.
{(3-3). (9. -6). (0-9)
b. {(3-3), (9. - 6), (3, - 2)}
c. {(3 - 3). (9. -6). (9. 2). (Q - 9)
d. {39.0 -4}
Please select the best answer from the choices provided
A
B

Answers

Answer:

A. (3,-3), (9, -6), (0,-9)

Step-by-step explanation:

a function has only one output value(y- values) for each input value(x- values)

Solve (3k - 1) (4k + 9) using the FOIL method. QUICK!

Answers

Answer:

12k^2 + 23k - 9

Need helpppppppppppppppp

Answers

Answer:

[tex]46\%[/tex]

Step-by-step explanation:

let the percentage be x

[tex] 37 \times x\% = 17\\ 37 \times \frac{x}{100} = 17 \\ \frac{37x}{100} = 17 \\ x = \frac{17 \times 100}{37} \\ x = 45.94\%[/tex]

3. Consider the graph of A, B, C and it’s image A’, B’, C’. What reflection produces this image?

Answers

Reflection over the y-axis

The rule for a reflection over the y-axis is (x,y)→(−x,y)

complete the soloution of the equation. find the value of y when x equals 0. -3x - 2y = -4

Answers

Answer:

-3×0 - 2 × y = -4

-2 × y = -4

y = -4/-2

y = 2

12.79 less than the product of 42 and x

Answers

Answer:

hdhdhdhdhd

Step-by-step explanation:

hhffhffjfj

Out of 350 students, 315 went
on the class field trip. What
percent of the students did
not go on the class field trip? Hurry! I need the answer asap!

Answers

Answer:

350-315=35

(35÷350)×100

=10%

Answer:

10%

Step-by-step explanation:

I subtracted the number of total students by the ones that went on the field trip.

350 - 315 = 35

35 students did not go on the field trip.

We can turn this into a fraction:

[tex]\frac{35}{350}[/tex]

[tex]\frac{35}{350}[/tex] = [tex]\frac{1}{10}[/tex]

[tex]\frac{1}{10}[/tex] = 10%

10% of students did not go on the class field trip.

7-9-0-0-0-0-0-0-0-0-0-0-6-6-6-6--6-6-6-6-6-6-6-6-6-6-6-

Answers

I believe The answer is -92

Answer:

It is -80

Step-by-step explanation:

u just subtract

write a decimal equivalent to the fraction
7/50

Answers

nfhfjfjfjfuvjgjgkfkfkfjfjgjgjgjgjgkgkgkgk

Answer:

0.14

бу - 13х + 10 = 4у 12

Answers

Answer:

13x + 42y = 10

Step-by-step explanation:

[tex]6y - 13x + 10 = 4y12[/tex]

[tex]6y - 13x + 10 = 48y[/tex]

[tex]6y - 13x - 48y = - 10[/tex]

[tex] - 42y - 13x = - 10[/tex]

[tex]42y + 13x = 10[/tex]

[tex] = 13x + 42y = 10[/tex]

A product of 9 and a number plus 1 is 19. Write an equation?

Answers

a number plus 1 is x+1
so the equation will be
9(x+1) = 19

Use an equation to describe its intersection with each of the coordinate planes. (If the sphere does not intersect with the plane, enter DNE.)

a. intersection with xy-plane
b. intersection with xz-plane
c. intersection with yz-plane

Answers

The question seems to be incomplete. I assume that we have the equation of a sphere, and we want to define equations of the intersection between that sphere and some given planes.

A general sphere of radius R centered at the point (a, b, c) is written as:

(x - a)^2 + (y - b)^2 + (z - c)^2 = R^2

Each of the planes will have a fixed value, to find the intersection, we just need to "fix" that fixed value in the equation above.

a) Intersection with xy-plane

The xy-plane has a z-value of 0 (the x and y values are free) so to write the intersection we only need to fixate z = 0.

Using the general sphere we get:

(x - a)^2 + (y - b)^2 + (0 - c)^2 = R^2

(x - a)^2 + (y - b)^2 + c^2 = R^2

(x - a)^2 + (y - b)^2 = R^2 -  c^2

This is a circle, centered at (a, b) in the xy-plane, and with a radius of:

√(R^2 - c^2)

Similarly:

b) intersection with xz-plane

Here we have y = 0, then the equation becomes:

(x - a)^2 + (0 - b)^2 + (z - c)^2 = R^2

(x - a)^2 +  b^2 + (z - c)^2 = R^2

(x - a)^2  + (z - c)^2 = R^2 - b^2

c) intersection with yz-plane

Here we have x = 0

(0 - a)^2 + (y - b)^2 + (z - c)^2 = R^2

a^2 + (y - b)^2 + (z - c)^2 = R^2

(y - b)^2 + (z - c)^2 = R^2 - a^2

Finally, in which cases we would write DNE?

Only if the expression at the right (the radius of the circle) are smaller than zero.

For example, if R^2 - a^2 < 0, then the sphere does not intersect the yz-plane.

If you want to learn more you can read:

https://brainly.com/question/9462569

Write 6×10 in expanded form using powers of 10 with exponents

Answers

Answer:

6 x [tex]10^{1}[/tex] exponential notation

or 60 standard notation

Step-by-step explanation:

Prove that the line that passes through (8, -1) and (4, -3) is parallel to the line that passes through (-6, -1) and (2, 3).

Answers

Answer:

Both lines have the same slope.

Step-by-step explanation:

- If two lines are parallel, they have the same slope. To prove that these, lines are parallel, we have to first find out the slope between points.

Line 1 :

y2 - y1 / x2 - x1

-3 - (-1) / 4 - 8

-2/-4

= 1/2

Line 2 :

y2 - y1 / x2 - x1

3 - (-1) /2 - (-6)

4/8

= 1/2

Both the lines have the same slope meaning they are parallel.

Write each rate as a fraction in lowest terms 30 feet in 5 seconds

Answers

Answer:

30 feet/5 seconds = 6 feet/1 second. hope this helps

Step-by-step explanation:

- Zombie

Answer: 6/1

Step-by-step explanation:

30/5= 6/1

(-2x^2yz^-2)^4 simplify the problem

Answers

Answer:

-8x(8yz)(-8)

Step-by-step explanation:

(-2x^2yz^-2)4

-8x(8yz)(-8)

simplify 3√578 - √162 + 4√32

Answers

[tex]3\sqrt{578}-\sqrt{162}+4\sqrt{32}=\\\\=3\sqrt{289\cdot2}-\sqrt{81\cdot2}+4\sqrt{16\cdot2}=\\\\=3\sqrt{17^2\cdot2}-\sqrt{9^2\cdot2}+4\sqrt{4^2\cdot2}=\\\\=3\cdot17\sqrt2-9\sqrt2+4\cdot4\sqrt2=\\\\=51\sqrt2-9\sqrt2+16\sqrt2=51\sqrt2+7\sqrt2=\boxed{58\sqrt2}[/tex]

Solve the equation for y.

3x+2y=6

Group of answer choices

y=9x/2




y=−3/2x+3




y=−3x+6




y=(3x)(6)/2

PLEASE HURRY

Answers

The correct answer is B Y=-3/2x +3

Answer:

[tex]3x + 2y = 6 \\ 6 - 3x = 2y \\ y = \frac{6 - 3x}{2} \\ \\ thank \: you[/tex]

A submarine left Diego Garcia and traveledtoward St. Vincent. Three hours later acruise ship left traveling at 16 km/h in aneffort to catch up to the submarine. Aftertraveling for five hours the cruise shipfinally caught up. What was the submarine's average speed

Answers

Average speed of submarine is 10 km/h

Given information;

Cruise ship left after 3 hours

Speed of cruise ship = 16 km / hour

Time taken by cruise ship = 5 hours

Find:

Average speed of submarine

Computation:

Distance = speed × time

Distance cover by cruise ship = 16 × 5

Distance cover by cruise ship = 80 km

So,

Distance cover by submarine also 80 km

So,

Time taken by submarine = 5 + 3

Time taken by submarine = 8 km

Average speed of submarine = 80 / 8

Average speed of submarine = 10 km/h

Learn more:

https://brainly.com/question/23774048?referrer=searchResults

You have $4150.in a cookie jar. Each month you spend half of the balance. How much do you have after 4 months? (Round your answer to the nearest cent.)
Enter a number
Need Help
Master it

Answers

Answer:

$259.4

Step-by-step explanation:

$4150/2

$2075/2

$1037.5/2

$518.75/2= $259.375

round to nearest cent = $259.4

The balance we have after four months is $259.4.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

You have $4150.in a cookie jar

Each month you spend half of the balance

Now,

Spent in 1 month=4150/2

=2075

Spent in 2 month=2075/2

=1037.5

Spent in 3 months=1037.5/2

=518.75

Spent in 4 months=518.75/2

=259.375

Therefore, answer of this algebra will be $259.4;

More about the Algebra link is given below;

brainly.com/question/953809

#SPJ2

What is 2x+2y=8 in standard form

Answers

Answer:

x+y=4

Step-by-step explanation:

2x+2y=8

By taking out 2 from 2x+2y as common terms, we get

2(x+y)=8

Now, by dividing both sides by 2, we get

2(x+y)/2=8)2

x+y=4

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