Answer:
C
Step-by-step explanation:
We are given the function.
[tex]h(x)=e^{2x}[/tex]
And we want to find its inverse.
Let's switch h(x) and x and change h(x) to h⁻¹(x). Hence solve:
[tex]\displaystyle \begin{aligned} x & = e^{2h^{-1}(x)} \\ \\ \ln x & = \ln e^{2h^{-1}(x)} \\ \\ \ln x & = 2h^{-1}(x) \\ \\ h^{-1}(x) & = \frac{1}{2} \ln x\end{aligned}[/tex]
In conclusion, our answer is C.
Note:
[tex]\ln(x)=\log_ex[/tex]
Why does the number 26 not belong with 17, 26, 44 & 65?
Answer & Step-by-step explanation:
This is what is called an arithmetic sequence. An arithmetic sequence adds the same number every time. If we take and subtract the 3rd term from the 4th term, we get 21. However, when we subtract 17 from 26 or 26 from 44, we get 9 and 18 respectively, which is not in keeping with the sequence.
___________________________________________________I AM ALWAYS HAPPY TO HELP :)Given the function: f(x) = x2 – 2x How can you restrict the domain so that f(x) has an inverse? What is the equation of the inverse function?
Answer:
B
Step-by-step explanation:
got it right on edge
The domain restriction is x ≥ 1 and inverse function is f⁻¹(x) = 1+√(x+1)
What is Inverse of Function?An inverse function is a function that returns the original value for which a function has given the output. If f(x) is a function which gives output y, then the inverse function of y, i.e. f-1(y) will return the value x.
Given:
f(x) = x² – 2x
We can find the inverse function by solving for y:
x = f(y)
x = y² -2y
x +1 = y² -2y +1
x +1 = (y -1)²
√(x +1) = y -1
1 +√(x +1) = y
So, the inverse function is
[tex]f^{-1}[/tex](x) = 1 +√(x +1)
Thus, the minimum value of x for which the original function has this as an inverse is 1.
So, The domain restriction is x ≥ 1 and inverse function is f⁻¹(x) = 1+√(x+1)
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a kit contains 600 letter tiles and 40 number tiles each tile has the same mass and the kit has a total mass of 2400 grams. what equation would represent this
Answer:
900
Step-by-step explanation:
5th GRADE MATH! Select the statement that correctly compares two numbers. A. 6,092 > 6,092.001 B. 6,197.02 > 6,197.2 .C 6,232.01 = 6,232.1 D. 6,365.1 < 6,365.999
Answer:
D is correct
Step-by-step explanation:
A is incorrect because the lesser than is .001 higher
B is wrong since is .18 higher
C is wrong because its not equalone is .9 higher
Answer:
D
Step-by-step explanation:
6365.1<6365.999
a temperature recorded in Antarctica was -122 F. The temperature recorded in the desert was 133 F. how many degrees warmer is 133 F than 122 F
Answer:
255 F
Step-by-step explanation:
133 + 122 = 225.
So that is the answer.
133°F is 255 degrees warmer than -122°F.
To find out how many degrees warmer 133°F is than -122°F, we can subtract the two temperatures:
Temperature difference = 133°F - (-122°F)
Remember that subtracting a negative number is the same as adding its positive value, so the calculation becomes:
Temperature difference = 133°F + 122°F
Temperature difference = 255°F
So, 133°F is 255 degrees warmer than -122°F.
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For what x-values is the function positive? Select all that apply.
A-5
B. 0
C. 3
D. 3.5
Answer: A and D
Step-by-step explanation:
The function is positive when the graph is above the x-axis.
in the image we can see that the graph is above in between the points:
x = - 5 and x = 0, then goes bellow, and then comes up again at x = 3.5 and the graph ends at x = 4.
Then the regions where the function is positive are:
-5 < x < 0 and 3.5 < x < 4
Then the correct options are:
A and D
I don't understand how to solve this, please help!
Answer:
x+1 , x<-1
x²-bx-4 , -1≤x≤4
1/2 x +a
substitute x=-1 , continuous everywhere
x+1=x²-bx-4 when x=-1
-1+1=-1²-b-4
1+b-4=0 ⇒ +b-3 ⇒ b=3then for :
x²-bx-4=1/2 x +a for x=4
4²-4b-4=1/2x+a
16-4(3)-4=4/2+a
16-12-4-2=a
a=-2the equations will be :
x+1
x²-3x-4
1/2x-2
I hope this help
the original recipe called for 3/8 cup of blueberries what is the ratio of blueberries to butter in the recipe? how many cups of blueberries are needed in the new enlarged mixture?
i'll mark the brainlest!!!
Answer:
If the recipe calls for 5/8 cup of butter, the ratio would be 3:5 (blueberries to butter), if the recipe was enlarged you can use the same method and find out the new ratio
In the figure below, B lies between A and C. Find the location of B so that AB is 1/8 of AC.
Answer:
-3
Step-by-step explanation:
first do -22-2= -24
then do 1/8 of -24= -3
On a train the ratio of children to adults is 7:4 If there are 63 children on the train how many adults are on the train
Answer:
let the number of children and adult be 7x and 4x
as per question
7x=63
x=63/7=9
no. of adult= 4x= 4*9=36
Step-by-step explanation:
You collect a total of $75 in donations from three people. The three donations are in the ratio 4 to 4 to 7. How much is each of the smaller donations? And how much greater is the largest donation then one of the smaller donations?
How can you use a number line to find the sum of -4 and 6?
Answer:
see explanation for number line\ $29$
Step-by-step explanation:
this is the answer guys.
Simply the expression 3(2x+5)
Answer:
6x+15
Step-by-step explanation:
(3) (2x+5)
(3) (2x) + (3) (5)
What is 12 -(-3) = and how do you get that answer?
Answer:
15
Step-by-step explanation:
Step 1:
12 + 3
Answer:
15
Two negative signs cancel out and turns it into addition.
Hope This Helps :)
Solve the literal equation for the given variable.
n = 4/5(m+7);m
Answer:
[tex]m = (5n/4) -7[/tex]
Step-by-step explanation:
[tex]n = 4/5(m + 7);m\\(5)n = 4(m + 7)\\5n/4 = m + 7\\m = (5n/4)/7[/tex]
Emma already has read 6 of 20 books on her summer reading list. What percent of the books on her list has she read already.
Answer: 30%
Step-by-step explanation:
5(2x - 8) = 90
A.5
B.10
C.13
D.15
Answer:
13
Step-by-step explanation:
5 (2x - 8) = 90
5 × 2x - 8 = 90
2x - 8 = 90 ÷ 5
2x - 8 = 18
2x = 18 + 8
2x = 26
2x/2 = 26/2
x = 13
13 is the answer to the question.
4. The midpoint of XY is (3, -5). The coordinates of point X are (1,5).
What are the coordinates of point Y?
Answer:
(5,-15)
Step-by-step explanation:
X to the midpoint, the x coordinate goes up 2 and the y coordinate goes down 10. So from the midpoint to Y, the x coordinate must go up 2 (making it 5) and the y coordinate goes down 10 (making it -15)
Is the number 3,600−−−−−√ rational or irrational?
Answer:
It's Rational.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
What is the solution to this equation?
X- 15 = -6
A. x= -9
B. x = 21
C. x= -21
D. x = 9
Answer: [tex]x=9[/tex]
Add 15 to both sides
[tex]x-15+15=-6+15\\x=9[/tex]
Steps to solve:
x - 15 = -6
~Add 15 to both sides
x = 9
Best of Luck!
is 5.676677666777 a rational number? ( please just a yes or no and please explain is easy terms, i'm stupid. )
Yes.
Step-by-step explanation:
Im pretty sure about this but there's the possibility that I'm wrong.
A number that can be changed into a fraction is a rational number.
So any decimal that terminates (Ends) or repeats (has the same numbers forever.) are in fact rational numbers.
Find F(10) in father function f(x) =-2x+4
Need answers ASAP
Please Help
The expression (y – 9)2 is equivalent to which expression. Simplify and write in standard form. Show your work.
Answer:
2y-18
Step-by-step explanation:
(y-9)2 -----Distributive property
2*y=2y
2*9=18
=2*y-2*9
=2y-18
Hope this helps ;) ❤❤❤
Answer:
yes
Step-by-step explanation:
A salesman packs dog biscuits in boxes containing 16, 17, 23, or 24 pounds each. He will not sell them in any other sizes or split a box. A customer wants exactly 100 pounds ofthe biscuits, no more or no less. Can the salesman fill the order? If not, how close can he come to making up the 100 pounds? He has as many of each size box as he might need.
Answer:
the closest the sales man can fit in a box is 96lbs without going over. so therefore, no, he cannot fulfill the order.
F(4)= If g(x)=2,x=.??
Answer:
f(4) = -10
x = 0
Step-by-step explanation:
From the graph attached,
For x = 4,
Value of the function will be,
f(4) = y value at x = 4
f(4) = -10
Similarly, for y = g(x) = 2,
x value of the function will be,
x = 0
For which g(0) = 2
Therefore, for x = 0 value of the function will be 2.
g(0) = 2
Answer:
f(4) = -10
Step-by-step explanation:
18= 5r +-3 (p+9)
How do I solve this
Remove the parentheses, Move the terms, Calculate, Divide both sides, write in parametric form.
Answer should be r = 3/5p + 9, pER
salma sang 4 songs each song was 5/8 minutes long for how much time did she sing in total?
Answer:
2 1/2 minutes
Step-by-step explanation:
5/8 + 5/8 + 5/8 + 5/8
20/8
2 and 4/8 minutes
Please help me solve all three of these..
Answer:
5: x=27 (Positive)
8: x=9 (9 positive not negative)
11: x=24 (Positive not negative)
Step-by-step explanation:
5: 9*3=27 so 27/9
8: 38+7=45 45/5=9 so x=9
11: 15-7=8 8*3=24, 24/3-15=-7 so x=24
What are the terms in the expression, 2 + 6 + 10b - 8a?
a. 2, 6, 10b, and 8a.
b. 2, 6 , 10b, and -8a.
c. 2 + 6 and 10b - 8a.
Answer:
B
Step-by-step explanation:
Option b is our correct answer.
2, 6 , 10b, and -8a.
Given,
2 + 6 + 10b - 8a
We need to find the terms in the expression.
What are terms in an expression?Every expression is made of terms.
Example:
ax² + bx + c + d
ax², bx, c and d are the four terms that make the expression.
Example:
ax² - bx - c - d
ax², - bx, - c and - d are the terms in the expression.
Remember to take the sign along with the terms.
Find the terms in the expression.
We have,
2 + 6 + 10b - 8a
2 - one expression
6 - one expression
10b - one expression
-8a - one expression
Thus,
Option b is our correct answer.
2, 6 , 10b, and -8a.
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9k - 12 - 8k + 10 - 5k Please help and go fast I have limited time
Answer:
-4k-2
Step-by-step explanation: