Answers
[tex]\boxed{\boxed{\pink{\sf \leadsto Hence \ the \ Inverse \ of \ the \ given \ function \ is \ x^2+2x-4 .}}}[/tex]
Step-by-step explanation:A function is given to us , and we need to find its inverse. So the function is ,
[tex]\bf\implies f(x) = \sqrt{x + 5 } - 1 [/tex]
So , firstly replace x with y in the given function and then solve for y to get its inverse . Taking the given function ,
[tex]\bf \implies f(x) = \sqrt{x+5}-1\\\\\bf\implies y = \sqrt{x+5}-1 \\\\\bf\implies x = \sqrt{y+5}-1 \:\:\bigg\lgroup \red{\sf Replacing \ x \ with \ y .} \bigg\rgroup \\\\\bf\implies x + 1 = \sqrt{y+5}\\\\\bf\implies y+5 = (x+1)^2 \\\\\bf\implies y+5 = x^2+1 +2x \\\\\bf\implies y = x^2+1-5+2x \\\\\bf\implies y = x^2-4+2x \\\\\bf\implies \boxed{\red{\bf f^{-1}(x)= x^2+2x - 4 }}[/tex]
Here I have also attached the graph of , x² + 2x - 4 and √(x+5) - 1. Here blue graph is of √(x+5) - 1 & red of x²+2x-4.
Hence the inverse f -¹(x) of the given function is x² + 2x - 4 .
Related Questions
how do i answer this please?
Answers
Answer:
a) [tex]5\sqrt{3} + 3\sqrt{5}[/tex]
b) [tex]4(\sqrt{2} + \sqrt{7})[/tex]
Step-by-step explanation:
a) [tex]9\sqrt{3} - 4\sqrt{3} +\sqrt{5} + 2\sqrt{5}[/tex]
Taking √3 & √5 common respectively,
[tex]=> \sqrt{3} (9 - 4) + \sqrt{5} (1 + 2)[/tex]
[tex]=> 5\sqrt{3} + 3\sqrt{5}[/tex]
b) [tex]10\sqrt{2} + 4\sqrt{7} - 6\sqrt{2}[/tex]
Taking √2 common ,
[tex]=> \sqrt{2} (10-6) + 4\sqrt{7}[/tex]
[tex]=> 4\sqrt{2} + 4\sqrt{7}[/tex]
Taking 4 common ,
[tex]=> 4(\sqrt{2} + \sqrt{7})[/tex]
A cyclist travels 4miles in 15 minutes. What is her average speed in mph?
Answers
Answer:
5
Step-by-step explanation:
Hence, the average speed to the cyclist is 16mph.
What is speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
How to solve?We know,
distance covered = 4 miles
time taken = 15 minutes = [tex]\frac{1}{4}[/tex]hours
speed = [tex]\frac{4}{\frac{1}{4} }[/tex] = 16
Hence, speed is 16.
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Write these in order, smallest first 0.34 1/3 3.5%
Answers
Answer:
1/3,0.34,3.5%
Step-by-step explanation:
Answer:
3.5, 1/3, 0.34
Step-by-step explanation:
3.5 as a fraction is 7/2 and 0.34 as a fraction is 7/20
Triangle ABC has vertices A(-4, 1), B (-1, 3) and C (-1, 1). what would the vertices be if you graphed it’s reflection over the y axis
Answers
If this coordinates are reflected over the y-axis the resulting coordinate will be at A'(4, 1), B'(1, 3) and C'(1, 1)
Generally, if a coordinate (x, y) is reflected over the y-axis, the coordinate of the pre-image is (-x, y).
Note that the x-coordinate was negated while the y-coordinate remain the same.
Given the coordinate vertices of a triangle A(-4, 1), B (-1, 3) and C (-1, 1), if these coordinates are reflected over the y-axis the resulting coordinate will be at A'(4, 1), B'(1, 3) and C'(1, 1)
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What is the length of the the midsegment of a trapezoid with bases of length 14 and 22?
The length of the midsegment of a trapezoid with the given bases is
Answers
Answer:
it would be about 138 for the hole thing
Step-by-step explanation:
Factor: -12n - 20 they are asking for an expression
Answers
Answer:
-4(3n+5)
Step-by-step explanation:
Factored -4 out of -12n-20. Let me know if this answers the question!
which statement best describes this graph?
Answers
Answer:
the second one
Step-by-step explanation:
You burn 5 calories each minute you bike. What integer represents the change in your calories
after you bike for 30 minutes?Immersive Reader
Answers
Answer:
150
Step-by-step explanation:
what is the variable in 5 + 12w
Answers
the variable in this question would be........................ W
you are welcom
what is 9.76 with 8% tax
Answers
Look at the system of equations:
2x + 6y = 10
5x + 15y =25
(HINT: solve for y=mx+b to graph!)
Which of these statements is correct?
A. The system has no solution
B. The system has an infinite number of solutions
C. The system has one solution at (-1,2)
D. The system has one solution at (5,0)
Answers
Answer:
B
Step-by-step explanation:
Both C and D solve the equations, so the system must have infinite solutions.
Tell which number is greater.
0.086, 86%
Answers
Answer:
86%
Step-by-step explanation:
Explanation
86% as decimal = 86/100 = .86
Now u can tell that .86> .086
Please provide the answer and an explanation.
Answers
Answer:
A = 37.1 square cm
Step-by-step explanation:
Composite Figures
The image shows a figure that can be seen as a composition of three regular shapes: two identical rectangles and a quarter of a circle.
The area of a rectangle of dimensions W and L is:
Ar = WL
And the area of a circle of radius r is:
[tex]Ac =\pi r^2[/tex]
A quarter of a circle has an area of:
[tex]\displaystyle A_q =\frac{\pi r^2}{4}[/tex]
The rectangles have dimensions of 5 cm by 3 cm, thus the area is:
Ar = 5 cm * 3 cm = 15 square cm
The quarter of a circle has a radius of r=3 cm, its area is:
[tex]\displaystyle A_q =\frac{\pi 3^2}{4}[/tex]
Calculating:
[tex]\displaystyle A_q =7.07\text{ square cm}[/tex]
The total area is twice the area of each rectangle plus the area of the quarter of a circle:
A = 2*15 + 7.07
A = 37.07 square cm
To the nearest tenth:
A = 37.1 square cm
What is the value of x
Answers
Answer:
Step-by-step explanation:
Add all number together and take the square root
A 52 foot piece of fishing line needs to be cut into 2 1/2 sections to make as many fishing rods as possible. How much of the fishing line will be left over?
Answers
please help asap I’m going to fail if I don’t ace this and brainly doesn’t have this question if anyone knows how to do this I will cashapp you
Answers
Answer:
C
Step-by-step explanation:
a translation over the x-axis keeps the same x value but flips the y value (makes it the opposite.)
so here, C starts at point (1,-2). when reflected over the x-axis this becomes (1,2)
a translation to the left subtracts from the x value
the coordinate changes from (1,2) to (-2,2) because 3 is subtracted from 1
how do i work this out please?
Answers
Answer:
[tex]5 \sqrt{5} - 2 \sqrt{5} = 3 \sqrt{5} \\ 8 \sqrt{7} + 3 \sqrt{7} = 11 \sqrt{7} [/tex]
hope this helps.
Answer:
[tex]11 \sqrt{7} [/tex]
Step-by-step explanation:
[tex]8 \sqrt{7} + 3 \sqrt{7} [/tex]
[tex] \sqrt{7} (8 + 3) [/tex]
[tex]11 \sqrt{7} [/tex]
PLEASE HELP!!!
Which algebraic expression is a polynomial with a degree of 3?
A) 4x3 – StartFraction 2 Over x EndFraction
B) 2y3 + 5y2 – 5y
C) 3y3 – StartRoot 4 y EndRoot
D) –xyStartRoot 6 EndRoot
Answers
Answer: B. 2y3 + 5y2 – 5y
Step-by-step explanation: From the expression 2y3 + 5y2 – 5y, the highest degree of the polynomial is 3. Hence, 2y3 + 5y2 – 5y is a polynomial with a degree of 3.
Answer:
the person on top is right its B
Step-by-step explanation:
but i got it because the assignment on edge said it's right
PLEASE HELP ASAP I REALLY NEED IT
Answers
Answer:
81
Step-by-step explanation:
8^2 + 2 * 8 + 1
= 64 + 16 + 1
= 80 + 1
= 81
What is the slope of the line that passes through (3,5) (7,3)
Answers
I am 90% sure that is correct
The sum of all the solutions of the equation: (10x − 3a )(3x + 39)(5x − 3) = 0 is (
− 1).
Find a.
Please help!!
Answers
2627828818182-718818288281-288181991_2792901=72892992
Answer:
[tex](10x - 3a)(3x + 39)(5x - 3) = 0 \\ dealing \: with \: (10x - 3a) \: and \: (5x - 3) \\ (10x - 3a)(5x - 3) = 0 \\ 50 {x}^{2} - (30 + 15a)x + 9a = 0 \\ sum \: of \: the \: equation \: = (30 + 15a) = - 1 \\ 15a = - 31 \\ a = - \frac{31}{15} [/tex]
The orbit of the Moon around the Earth is an ellipse with Earth at one focus. If the length of the major axis of the orbit is 477,736 miles and the length of the minor axis is 477,078 miles, find the minimum and maximum distances from Earth to the Moon. Round to the nearest whole number.
Answers
Answer:
226,335
251,401
Step-by-step explanation:
SKR SKR BOW
The minimum distance from Earth to Moon is 226,332 miles
The maximum distance from Earth to Moon is 251,401 miles
What is an Ellipse?
An ellipse is created by a plane intersecting a cone at the angle of its base
All ellipses have two foci, a center, and a major and minor axis
The sum of the distances from any point on the ellipse to the two foci gives a constant value
The value of eccentricity for all ellipses is less than one
The standard for of equation of ellipse is
( x²/a² ) + ( y²/b² ) = 1
where a > b
The length of the major axis = 2a
The length of the minor axis = 2b
The coordinates of foci = ( ±c , 0 )
where c² = a² - b²
Given data ,
The orbit of the Moon around the Earth is an ellipse with Earth at one focus
The length of the major axis 2a = 477,736 miles
The length of the minor axis 2b = 477,078 miles
Now , the value of a = 238,868 miles
The value of b = 238,539
Now , the maximum distance from earth to moon is = a + c
The minimum distance from earth to moon is = a - c
The value of the foci is given by c² = a² - b²
Substituting the values in the equation , we get
c² = ( 238,868 )² - ( 238,539 )²
c² = 157066903
Taking square roots on both sides , we get
c = 12532.63 miles
Now , maximum distance from earth to moon is = a + c
Maximum distance = 238,868 + 12535.63
= 251,400.63 miles
≈ 251,401 miles
Now , The minimum distance from earth to moon is = a - c
Minimum distance = 238,868 - 12535.63
= 226,332.37 miles
≈ 226,332 miles
Hence ,
The minimum distance from Earth to Moon is 226,332 miles
The maximum distance from Earth to Moon is 251,401 miles
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Which point is a solution of the inequality 5x – 2y > -4?
A= (-4,-8)
B= (-2,-9)
C= (-4,5)
D= (-6,3)
Answers
Answer is Option-B
What is Inequality:
A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Here, when we substitute B = (-2, -9) in given inequality equation i.e.,
5(-2) - 2(-9) > -4
-10 + 18 > -4
8 > -4 (Satisfied)
Others options won't satisfies.
Answer is Option-B
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please help . me . i will even help . you mark you brainliest
Answers
A = Not sure
B= 12.0
Hope I helped
Mrs. Jones bought 250 apples for $22 500. She sold 50 for $120 each, and the remain
she sold 5 for $1 000 a parcel.
(a) State whether she made a profit or loss.
(b) Calculate her percentage profit or percentage loss.
Answers
Step-by-step explanation:
Answer:
(a) yes
(b) 104% profit
Step-by-step explanation:
250 apples for $22,500
Part 1:
50x$120=$6000
Part 2:
200 sold at $1000 per 5 apples=200/5x1000=$40,000
$40,000+$6000=$46,000
A profit of $23,500
23500/22500=1.044 or 104% profit
Step-by-step explanation:
Guys I rlly need help this due in 4 minutes, whats 1683 divided by 383 please help me
Answers
Answer:
1683 / 383 = 4.39 or approx 4.4
Answer:
4.39425587467 or 4 remainder 151.
Step-by-step explanation:
Long division.
What is the value of s?
Answers
Step-by-step explanation:
Sum of angles in a triangle = 180°.
=> s° + (s/7 + 3)° + (s/7 - 3)° = 180°
=> 9/7 * s° = 180°
=> s° = 180° * (7/9) = 140°
Hence the value of s is 140.
5x-2y=30 complete the missing solution to the equation
Answers
Answer:
I would have to go with x = 8 and y = 5, meaning the solution is (8, 5).
Step-by-step explanation:
[tex]5x - 2y = 30[/tex]
[tex]5(8) - 2(5) = 30[/tex]
[tex]40 - 10 = 30[/tex]
[tex]30 = 30[/tex]
Step-by-step explanation:
In terms of y=mx+b, we are to make the Y by itself.
Step 1. -2y = -5x +30
Make y become positive!
Step 2. 2y = 5x - 30
Distribut the 2 over to make it 1y.
Step 3. 1y = 5/2x - 15
The equation is y=5/2x - 15
If you are to find X it would be....
-15 divided by 2.5 gets you x= -6
find the value of sin 0 in each of the following figures.
Answers
Answer:
sinθ = [tex]\frac{8}{10}[/tex]
Step-by-step explanation:
sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{8}{10}[/tex]
Answer:
sin theta=p/h
=BC/AC
=8cm/10cm
=4cm/5cm
Hope it helps you.
A sales person at a Jewwlry store earns 5% commission each week. last week ,Heidi sold $640 worth of jewelry. Home much did she make in commission? How much did the jewellery store make from her sale?
Answers
Answer:
224
Step-by-step explanation:
5 percent of 640=32
32 times by 7=224