Answers
Hi!
We can see here that this is a composition question.
And since the composition of g of f of x is x, we can conclude that g(x) is the inverse of f(x) (if you're confused, search up the definition of an inverse function).
To find an inverse function, we can take the f(x) function and change the positions of the x and y variables.
[tex]f(x)=\frac{e^7^x+\sqrt{3}}{2}[/tex]
[tex]y=\frac{e^7^x+\sqrt{3}}{2}[/tex]
[tex]x=\frac{e^7^y+\sqrt{3}}{2}[/tex]
[tex]2x=e^7^y+\sqrt{3}[/tex]
[tex]e^7^y=2x-\sqrt{3}[/tex]
[tex]7y=ln(2x-\sqrt{3})[/tex]
[tex]y=\frac{ln(2x-\sqrt{3})}{7}[/tex]
Which is answer choice A, to check your work, you can solve the composition of g(f(x)), which will get you x.
[tex]g(f(x))[/tex]
[tex]g(\frac{e^7^x+\sqrt{3}}{2})[/tex]
[tex]\frac{ln(2(\frac{e^7^x+\sqrt{3}}{2})-\sqrt{3}}{7}[/tex]
2s cancel.
[tex]\frac{ln(e^7^x+\sqrt{3})-\sqrt{3}}{7}[/tex]
The natural log and e cancel.
[tex]\frac{7x+\sqrt{3}-\sqrt{3}}{7}[/tex]
[tex]\sqrt{3}[/tex]s cancel.
[tex]\frac{7x}{7}[/tex]
7s cancel.
[tex]x[/tex]
Hope this helps!
Related Questions
Please Help Me With This Math. It's 4th Grade Math!!!
Answers
Answer:
1 1/2 hours
=
Other ways to show would be; = 1 1/2 hours = 1 .5 hrs = 90 minutes
Step-by-step explanation:
We write out the question 2 1/4 - 3/4 = ?
Then you use the model A below
Next you can add on from the smaller number 3/4 being step 1
And you use model B to find step 2 + step 3 as it reminds you that there is 1/4 in total time being the smallest box out of the sum.
step 1 = 3/4 + 1/4 = 1 = 1/4 is missing in A model box
step 2 = + 1 (to make 2) = 1 is left in B model box
step 3 is + 1/4 is left in B model box
Then add the up = 1/4 + 1 + 1/4 = 1 1/2
Your answers will be model represents 3hrs divided into 6 hours
Jessi played in the afternoon
Playedi n afternoon for 1 1/2 hours
Answer:
1 1/2 hours
Step-by-step explanation:
[tex]16z - (-12z) =[/tex]
Answers
Answer:
4
Step-by-step explanation:
Please help! I need this fast!
Answers
Answer:
E. (6,4
F. (4,6)
G. (3,0)
H. (0,3)
Step-by-step explanation:
Handy Dandy grocery is having a sale this week. If you buy a five pound bag of apples for the regular price $2.99. You can get another bag for $1.79.
Answers
Answer:
The answer is below
Step-by-step explanation:
A grocery store is having a sale this week. If you buy a 5-pound bag of apples for the regular price, you can get another bag for $1.79. If you buy a 5-pound bag of oranges at the regular price, you can get another bag for $2.49. Write an equation to find the discount for each situation.
Regular price for apples is $2.99
Regular price for oranges is $3.99
Solution:
The original price of the apples = $2.99 , price at a discount = $1.79
Discount for A= original price - price at a discount = $2.99 - $1.79
Discount for A= $1.20
x = ($1.79 / $2.99) * 100% = 59.9%
Discount in percentage = 100% - 59.9% = 40.1%
The original price of the orange = $3.99 , price at a discount = $2.49
Discount for R = original price - price at a discount = $3.99 - $2.49
Discount for R = $1.50
x = ($2.49 / $3.99) * 100% = 62.4%
Discount in percentage = 100% - 62.4% = 37.6%
Jami deposits $800 in her bank account which collects 2% interest annually. How much total money will she have in her bank account after three years?
Answers
Answer:
$848
Step-by-step explanation:
800 x .02 x 3
800 is the input
.02 is the interest but rule is to move the decimal over
3 is the 3 years
I checked this with an interest calculator and its correct
https://www.dollartimes.com/savings/800
^thats the interest calculator if u need u can copy paste into ur browser^
Answer:
$848
Step-by-step explanation:
what is the slope of the line in the graph shown below ?
Answers
Answer:
-1/4
Step-by-step explanation:
The line is going down to the right so it is negative and the rise and run from seems to be rise 1, run 4 units, so the slope is rise/run so - 1/4
The perimeter of a rectangle is 36 meters. If the length of the rectangle is 10 meters, what is the width (in meters)?
Answers
find the value of given expression
[tex] \sqrt{56 - 7} [/tex]
Answers
Answer:
± 7
Step-by-step explanation:
Given
[tex]\sqrt{56-7}[/tex]
= [tex]\sqrt{49}[/tex]
= + 7 or - 7 , that is ± 7
Answer:
±7
Step-by-step explanation:
56 - 57
______
gives you 49
which then turns into ±7
⇒⇒⇒Hope this helps!
Solve for x*
please help
Answers
Answer:
B
Step-by-step explanation:
∠ AEB and ∠ ADC are corresponding angles and are congruent, then
3x - 10 = x + 40 ( subtract x from both sides )
2x - 10 = 40 ( add 10 to both sides )
2x = 50 ( divide both sides by 2 )
x = 25
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answers
Answer:
Step-by-step explanation:
Calculate the area of the base (which is a circle) by using the equation πr² where r is the radius of the circle. Then, multiply the area of the base by the height of the cylinder to find the volume.
Answer:
[tex]\frac{32}{3} \pi \\v= 33.5[/tex]
Step-by-step explanation:
[tex]v=\frac{4}{3} \pi r^{3}[/tex]
[tex]v= \frac{4}{3} \pi 2^{3} \\\\v=\frac{4}{3} \pi 8\\v=\frac{32}{3} \pi \\v= 33.5[/tex]
I will give you brainilest.
You might think that the angle between the hour and minute hand at 2:20 is 60 degrees, but it is not! The hour hand has moved beyond the 2. Calculate the angle between the clock hands at 2:20.
Answers
Answer:
70 degrees
Step-by-step explanation:
Moving from one hour number to the next (12 to 1, 3 to 4, etc) moves the hand of the clock 30 degrees. Using this, we know that the hour hand moved 60 degrees to get to the hour number 2. Then, the angle the hour hand moved because of the minute hand can be calculated by doing (20/60)*30=10. So the final answer would be 70 degrees.
Use the simple interest formula to find the interest earned and the ending balance. I = Prt
1. $48,000 at 3% for 6 years
Answers
Answer:
8640
Step-by-step explanation:
I = Prt
I = (48000)(0.03)(6)
I = 8640
How many hours do Max and Sasha exercise per week?
Max and Sasha exercise a total of 20 hours each
week. Max exercises 15 hours less than 4 times
the number of hours Sasha exercises. The system
x+y= 20
of equations
x - 4y = --15
represents this
situation, where x represents the number of hours
Max exercises and y represents the number of
hours Sasha exercises. How many hours do Max
and Sasha exercise per week?
Answers
y = (x + 4)(x - 1) what is the x intercept
Answers
(−4,0), (1,0)
There hope this helped
x intercept the y coordinate is 0
0=(x+4)(x-1)
Since brackets are multiplying and =0 one bracket needs to add up to 0
either x+4=0 or x-1=0
x+4=0
x=-4
x-1=0
x=1
So coordinates are
(-4,0). AND (1,0)
write 24 minutes to 3 hours as a ratio in its simplest form
Answers
24:180
6:45
3:15
1:5
3 hours = 180 minutes
So, 24:180.
Simplified: 1:5
Hope this helps; have a great day!
help please :,)
The zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
Α.Rx) = (x + 6)(x-4)
B. Rx) = (x + 6)(x+4)
C.f(x) = (x - 6)(x + 4)
D.f(x) = (x-6)(x - 4)
Answers
Answer:
I think the answer is c
Step-by-step explanation: hope i was a help
Indicate whether each statement about linear functions A and B shown below is true or false by checking the appropriate box in the table.
Function A
Function B
2
3
4
3
2
11
15
19
+
5
<
Statement
True
False
The rates of change for both Function A and Function B are positive.
The rate of change for Function A is 3 times the rate of change for Function B.
The intercepts for both Function A and Function B are positive
Answers
Multiply
7x(x^- x+2)
Answers
Rewrite (7x−2) 2 (7x-2) 2 as (7x−2) (7x−2) (7x-2) (7x-2).
(7x−2) (7x−2) (7x-2) (7x-2)
Expand (7x−2)(7x−2)(7x-2)(7x-2) using the FOIL Method.
Apply the distributive property.
7x (7x−2) −2 (7x−2) 7x (7x-2)-2 (7x-2)
Apply the distributive property.
7x(7x)+7x⋅−2−2(7x−2)7x (7x)+7x⋅-2-2(7x-2)
Apply the distributive property.
7x(7x)+7x⋅−2−2(7x)−2⋅−27x(7x)+7x⋅-2-2(7x)-2⋅-2
Simplify and combine like terms.
Simplify each term.
Multiply xx by xx.
7⋅7x2+7x⋅−2−2(7x)−2⋅−27⋅7x2+7x⋅-2-2(7x)-2⋅-2
Multiply 77 by 77.
49x2+7x⋅−2−2(7x)−2⋅−249x2+7x⋅-2-2(7x)-2⋅-2
Multiply −2-2 by 77.
49x2−14x−2(7x)−2⋅−249x2-14x-2(7x)-2⋅-2
Multiply 77 by −2-2.
49x2−14x−14x−2⋅−249x2-14x-14x-2⋅-2
Multiply −2-2 by −2-2.
49x2−14x−14x+449x2-14x-14x+4
Subtract 14x14x from −14x-14x.
49x2−28x+4
PLEASE HELP ME IM BEGGING ITS DUE IN 10 MINUTES
Answers
Answer:
wow good luck mines due in 5 mins and im stuck hahah
Step-by-step explanation:
You have 192 grams of a radioactive kind of iodine. How much will be left
after 28 hours if its half-life is 7 hours?
Answers
Answer:
192/2= 96 g after 7h
96/2=48 g after 14h
48/2= 24 g after 21h
24/2= 12 g after 28hSolve the following 1/2a + b
If a=10 b = 7 *
Answers
Answer:
1/2 × 10 + 7
=5+7
=12
..................
Answer:
12
Step-by-step explanation:
1/2a+b=
1/2*10 + 7 =
5+7= 12
The product of , and the sum of a number and - 4 is less than or equal to 64.
What are all the possible values of the number? Show your work.
Answers
Answer:
6
Step-by-step explanation:
The vertex form of the equation of a parabola is y = 2(x+ 3)2 - 5.
What is the standard form of the equation?
Answers
Answer:
y = 2x² + 12x + 13
Step-by-step explanation:
In ΔCDE, the measure of ∠E=90°, the measure of ∠C=83°, and DE = 8.6 feet. Find the length of EC to the nearest tenth of a foot.
Answers
Answer : 1.0559≈1.1 feet
Zack drew a scale drawing of a house and its lot. The backyard is 15 inches wide in the drawing. The actual yard is 24 feet wide. What scale did Zack use for the drawing?
Answers
Answer:
5 ÷ 96Step-by-step explanation:
The scale is
15 in ÷ 24 feet = 15 in ÷ 24*12 in =15 in ÷ 288 in =5 in ÷ 96 in = 5 ÷ 96Convert 24ft to in
1ft=12in24ft=24(12)=288inScale used
15/2885/965:96Let f be differentiable such that f(-2)=3,f(3)=5, f'(-2)=4 and f'(3)=6. Let g be differentiable functions such that g(x)=f^-1 (x) for all x. What is the value of g'(3)
Answers
Answer:
[tex]g'(3)=\frac{1}{4}[/tex]
Step-by-step explanation:
There is a rule in calculus that tells us that:
[tex]g'[f(x)]=\frac{1}{f'(x)}[/tex]
In this case, we know that f(-2)=3, therefore:
g'(3)=g'(f(-2))
So, if we used the rule, we would get that:
[tex]g'[f(-2)]=\frac{1}{f'(-2)}[/tex]
we know that f'(-2)=4, so:
[tex]g'[f(-2)]=\frac{1}{4}[/tex]
or:
[tex]g'[3]=\frac{1}{4}[/tex]
7 inches, 8 inches, 9 inches will these lengths form a triangle
Answers
Answer:
Yes
Step-by-step explanation:
If we use the triangle inequality theorem, then we would have:
7+8 > 9
HOPEE THIS HELPS
A bird drops a stick to the ground from a height of 92 ft. The function
h= -167 +92 gives the stick's approximate height h above the ground, in feet,
after t seconds. Graph the function. At about what time does the stick hit the
ground? Use inequalities to describe a reasonable domain and range for the
function.
Answers
Answer:
B
Step-by-step explanation:
help asap please!!!!
M is the midpoint of AB. The coordinates of A are (-2,3) and the coordinates of M are (1,0). Fine the coordinates of the other endpoint, point B.
Answers
What is the surface area of a dome (a half sphere) with a radius of 6 meters?
72 pi meters squared
48 pi meters squared
24 pi meters squared
144 pi meters squared
Answers
Answer: 72π meters squared.
Step-by-step explanation: Given that the radius is 6 meters, use the sphere surface area formula to find the surface area of the half-sphere;
Replace the value in the formula: A=4πr² → A=4π6²Solve the exponent first: A=4π6² → A=4π36The order of the multiples does not affect the total, so we can multiply 4 times 36 first: A=4π36 → A=144π144π is the surface area of the whole sphere, so half the sphere will be 72π. In conclusion, the surface area of the dome will be 72π meters squared.