The function f(x)=x^2+2 is not one to one. Determine a restricted domain that makes it one to one and find the inverse function
Answers
Answer:
Hope it helped
Step-by-step explanation:
The restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
What is inverse of a function?An inverse function or an anti function is defined as a function, which can reverse into another function.
Now the given quadtratic function is,
f(x) = x² + 2
Now vertex of the given quadratic function is (0,2)
Thus the range of the function is [2,∞)
If we restrict the domain of this function to either (-∞,0} or [0.∞), it will become one to one function.
Now the inverse function is given as,
y = x² + 2
Upon interchanging x and y, we get:
x = y² + 2
⇒ y² = x - 2
or, y = ±[tex]\sqrt{x-2}[/tex]
Hence, the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
Thus, the restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
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Related Questions
all the number sets that apply to -4/5
Answers
-8/10,-12/15,-16/20,-20/25,-24/30,etc.
The number sets that apply to -4/5 is the fractions.
What is a fraction?Fractions represent the parts of a whole or collection of objects.
A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.
Now the given number is,
-4/5
-4/5 is a fraction. A fraction has two components numerator and denominator. This can positive or negative. Other example of fractions include 1/2,3/2,-5/2,-1/3.
The numbers who are not fractions are 0, 3, 6, 7.7.
Thus, the number sets that apply to -4/5 is the fractions.
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someone help me asap
Answers
Answer:
19/20 cups
Step-by-step explanation:
Add the amounts together
1/4 + 7/10
Get a common denominator of 20
1/4 *5/5 + 7/10 *2/2
5/20 + 14/20
19/20
Answer:
19/20
Step-by-step explanation:
find a common denominator then do the same with the numerator then add.
Please help me with my homework!!!!!!
Answers
Answer:
Step-by-step explanation:
Given that x = 3 and y = 2 we can figure these out
3x = 3x3 = 9
5y = 5 x 2 = 10
9+10=19
X times y - 1
3x2-1=5
X*+y* =
3x3+2x2 = 13
2x3*-2 =
2x3x3 - 2 = 16
-5x3+9
= -6
2x2-3+5+3*-3x2 =
9
write the equation of a line in slope intercept form y=mx+b m=6, (0,5)
Answers
Answer:
m is the slope so plug in y=6x+b
and b is the y intercept so the equation is y=6x+5
Step-by-step explanation:
4. Complete the following explanation to show that the sum of two rational numbers a
rational number.
Let a,b,c and d be integers. Let x and y be rational numbers. Consider the following
expression:
* = and y =
The above expressions represent the
If x + y = y + x
represents the
then, we can use the
to show that x +y = 3+. Using the rule for addition of
fractions to write an equivalent expression for x + y = 4+we obtain
The product of two integers results in an integer, so bd, ad and cb are all integers. Also.
since the sum of two integers results in an integer, ad + cb is an integer. Therefore,
xty is
Answers
Solve for W.
4w=5.12
Answers
Answer:
x =1.28
Step-by-step explanation:
4w=5.12
Divide each side by 4
4w/4 = 5.12/4
x =1.28
the quotient of 5+h and n+3
Answers
Answer:
5+h/n+3
Step-by-step explanation:
5+h is numerator
and n+3 is denominator
so you make it a fraction to get the quotient which is 5+h/n+3
A simple pulley with the give radius 4 in used to lift heavy objects is positioned 10 feet above ground level. Given that the pully rotates 720 degrees determine the height yo which the object is lifted.
Answers
9514 1404 393
Answer:
50.3 inches
Step-by-step explanation:
720 degrees is 2 full turns, or twice the circumference of the pulley. The circumference is given by ...
C = 2πr
C = 2π(4 in) = 8π in
Then 2 times that is ...
height lifted = 2(8π in) = 16π in ≈ 50.3 in
The object was lifted about 50.3 inches.
I need answers asap!!!!!!!
Answers
Step-by-step explanation:
with God everything is possible
explanation
because we go to church
What and why is the total amount 180 is it a triangle? Or something
Answers
Answer:
Yes it is
Step-by-step explanation:
when you add up all parts of a triangle they are equal to 180
Answer:
yes
Step-by-step explanation:
the sum of interior angles of a triangle is = to 180 degrees.(It's a geomatory theorem)
You have one box that is 1 4/11
feet tall and a second box that is 1.36 feet tall. Write the decimal expansion for
. If you stack the boxes, about how tall will the stack be?
Answers
The stacked boxes would be 2.72 feet tall
The height of the stacked box is the sum of the lengths of the two boxes
1 4/11 is a mixed number and it has to be converted to a decimal
A mixed number is a number that has a whole number and a proper fraction.
A proper fraction is a fraction is which the numerator is less than the denominator.
The whole number is 1 and the proper fraction is 4/11
To convert to a decimal, divide the numerator by the denominator. Add this number to the whole number
4/11 = 0.36
1 + 0.36 = 1.36 feet
Height of the stacked boxes = 1.36 + 1.36 = 2.72 feet
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Determine if the expression 8a – a4 is a polynomial or not. If it is a polynomial,
state the type and degree of the polynomial.
The given expression
va polynomial.
represents
does NOT
represent
attempt 1 out of 2 / problem 1 out of max 1
Answers
Answer:
Represents
Step-by-step explanation:
Going over the basic definition of polynomial, an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division, we can see that the expression is indeed a polynomial.
Help me please look at the pictures
Answers
20 PTS + Brainliest. Please find the size of the blue area, explain your work.
Answers
here is answer, hope u understand:)
The temperature reading that is halfway between −10 degrees and 40 degrees is ___ degrees.
If the temperature was −3 degrees in the morning and 8 degrees in the afternoon, the change in temperature during that time is ____ degrees.
If the temperature has been changing at a rate of −1.5 degrees each hour, and it is currently 5 degrees, the temperature 4 hours ago was ___ degrees.
If the temperature continues to change at this rate of −1.5 per hour, and it is currently 5 degrees, the temperature in 4 hours will be ____ degrees.
Answers
Answer:
30, +11, 11, -1
Step-by-step explanation:
-10 + 30 = 10, 40 - 30= 10
-3 + 11 = 8
5 + (1.5 x 4) = 11
5 - (1.5 x 4) = -1
(−2x + 8) + (−8x^2− 8x)
Answers
Answer:
-8x^2 -10x + 8
Step-by-step explanation:
there is no multiplying just adding
Please help!
Please do not just give the answer, also explain please because I need to know how to do this.
Find the value of X
Answers
Answer:
x = 6.5
Step-by-step explanation:
In order to solve this problem, you need to use trigonometry (sin, cosine, tangent).
Sin = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Tangent = opposite/adjacent
We need to use tangent in this case because 10 is the opposite side from the 57° angle, and x is right next to it, making it adjacent. So, our equation would look like this:
tan (57)° = 10/x
Multiply both sides by x
x (tan (57)°) = 10
Divide both sides by tan (57)°
10 / tan (57)° = 6.49408 = 6.5
Step-by-step explanation:
We are given two angles measures and one side. Notice the given angle and the side that is opposite to that given angle is given. We need to find side x. But can we also find the angle opposite of the side we are trying to find. Yes we can
Remeber that triangles interior angles add up to 180.
Remeber that triangles interior angles add up to 180.One angle measure 90 and the other measure is 57 so
[tex]90 + 57 + x = 180[/tex]
[tex]x = 33[/tex]
So the angle opposite of the side we are trying to find is 33.
Since we know two angles and two sides that are opposite of those two angles respectively, we can use what is called Law of Sines
[tex] \frac{b}{ \sin(b) } = \frac{c}{ \sin(c) } [/tex]
where the numerator are the side measures, and the denominator are the angle measures.
Plug in the respectively values. Angle 57 is opposite of 10 and Angle 33 is opposite of x.
[tex] \frac{10}{ \sin(57) } = \frac{x}{ \sin(33) } [/tex]
Multiply both sides by sin 33 to isolate x.
We get
[tex]x = 6.494[/tex]
Round if needed
In other words, apply law of sines when you have two angles and two sides that are opposite of those angles respectively.
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
6,2,2/3….
Find the 8th term.
Answers
Answer:
Just divide 2/3 by 3 (or multiply by 1/3), 6 times to get the answer.
Please help me I’m struggling! I’ll give a brainliest!!
Collinear points lie on the same line. Find the value of k for which the following points are collinear: (k,3), (-3,2), (-1,1)
Answers
Answer:
k=-5
Step-by-step explanation:
For the points to be collinear any two pair must have the same slope
We find the slope of the 2nd and 3rd points
=1-2/-1--3
=-1/2
Now finding the slope of the 1st and any other point say point 3
1-3/-1-k=-½
-2/-1-k=-½
-4=-1(-1-k)
-4=1+k
k=-4-1
k=-5
PROOF
if the first point is (-5,3)
slope of point 1 and 2
=2-3/-3--5
=-1/2
What is 50x30 I really need to know
Answers
Answer:
1500
Step-by-step explanation:
Basically 5*3 then add the two zeroes. One from 50 and 30.
Find the sum of
2x^2- 8x– 6 and 9x^2-8
Answers
Answer:
11x^2-8x-14
Step-by-step explanation:
(2x^2- 8x– 6)+(9x^2-8) = 11x^2-8x-14
Answer:
11x^2-8x-14
Step-by-step explanation:
2x^2- 8x– 6 and 9x^2-8
solution:
2x^2- 8x– 6 +(9x^2-8)
=2x^2-8x–6+9x^2-8
=2x^2+9x^2-8x-6-8
=11x^2-8x-14
Hello! I’ll take any help !!
Answers
Answer:
√73
Step-by-step explanation:
a^2+b^2=c^2
8^2+3^2=c^2
64+9=c^2
√73 =√c^2
√73 =c
What is the answer ?
Answers
Answer:
27
Step-by-step explanation:
36 divided by 4 equals 9 which is what the sea turtle can swim in 1 second. Multiply 9 by 3 and you'll get 27.
Answer:
Step-by-step explanation:
Can someone tell me the asnwer to this ASAP?
Answers
Answer:
[tex]2\sqrt{2} \\2[/tex]
Step-by-step explanation:
[tex]\sqrt{8} = \sqrt{4*2} = \sqrt{4} * \sqrt{2} = 2*\sqrt{2} = 2\sqrt{2} \\\\\sqrt[3]{8} = \sqrt{2*2*2} = 2[/tex]
Answer:
I noticed that [tex]\sqrt{8\\}[/tex] does not have 3 on it like the second one. And i wonder that the answers would be different from each other
[tex]2\sqrt{2}[/tex]
2
The student looks up the word count on his favorite book, if the book has pages that are 5.5 in. x 6.5 in. and 59,540 words how many pages is the book? (This sentence and picture combine.)
Answers
Answer:
199 pages
Step-by-step explanation:
The average number of words on the page is 300. Because there are 59,540 words and 59540/300 = 198.46 (approximately), there are 199 pages in the book (because the 0.46 pages would be the last page).
I need help please i reposted this question 2 times no one knows the answer.1
Answers
Answer:
12 Points
Step-by-step explanation:
Given an isosceles right triangle that is oriented so that it is sitting on its hypotenuse, and the length of the hypotenuse is 12 mm. What is the height (from the hypotenuse to the vertex of the two legs) of this triangle as it sits
Answers
Answer:
5,12,13
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
What is the volume of the following rectangula
prism?
4
units
3
23
units
4
Answers
SORRYYYYYYYYYYYYYYY I DONT KNOWWWWW
What is the domain in roster notation(numerical order) x= -2,-1,1,3,3 y=3,-3,0-3,3
Answers
Answer:
Domain is {x|x = -2, -1, 1, 3}
Step-by-step explanation:
I. When domain is x.value and renge is y.value
Got more question or something to discuss? leave comment below
Help me pls ?? 1. Suppose there is a raffle with numbered tickets 1 - 150. One ticket is randomly
drawn from a hat. Find the following probabilities:
A. Drawing an even number
B. Drawing a number greater than 100
C. Drawing an even prime number
D. Drawing a negative number
Answers
B = less likely / unlikely
C =less likely
D = Impossible
