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
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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Find the value of x.
A. 5.58
B. 9.14
C. 15.2
D. 10
PLEASE HELP!!! :(
Answer:
D. 10
Step-by-step explanation:
[tex]{ \sf{(12x + 12) \degree = 79\degree + (5x + 3)\degree}} \\ { \sf{ \{outer \: angle \: is \: equal \: to \: sum \: of \: inner \: angles \}}} \\ { \sf{12x - 5x = 79 + 3 - 12}} \\ { \sf{7x = 70}} \\ { \sf{x = 10}}[/tex]
Suppose the function H(t) gives the heart rate of a runner at various points in time during a 20 mile run. Describe an appropriate domain of this function. Include a description of the kinds of numbers in the domain as well as any limitations on their values.
.....................
y - 4 = 3. what is y = ???
Hi ;-)
[tex]y-4=3\\\\y=3+4\\\\\boxed{y=7}[/tex]
Answer: 7
.....7-4=3
Which expression is equivalent to 180?
Answer:
[tex] \sqrt{2.2.3.3.5} [/tex]
[tex]\sqrt{2.2.3.3.5}[/tex] is equivalent to [tex]\sqrt{180}[/tex]. Correct option is 1. First, we look for perfect square factors within 180. We can factor 180 as follows: [tex]\(180 = 2^2 \times 3^2 \times 5\)[/tex]
Next, we can group the perfect square factors together:
[tex]\(180 = (2 \times 3)^2 \times 5\)[/tex]
Since we are taking the square root of 180, we can rewrite it as the square root of its perfect square factors multiplied by the remaining non-perfect square factor:[tex]\(\sqrt{180} = \sqrt{(2 \times 3)^2 \times 5}\)[/tex]
The square root of a perfect square is just the value of the number itself:
[tex]\(\sqrt{180} = 2 \times 3 \times \sqrt{5}\)[/tex]
Finally, we can simplify the expression by multiplying the numbers outside the square root [tex]\(\sqrt{180} = 6\sqrt{5}\)[/tex]
So, the expression [tex]\(6\sqrt{5}\)[/tex] is equivalent to [tex]\(\sqrt{180}\)[/tex], and it represents the positive square root of 180 with any perfect square factors taken outside the square root sign.
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0.6m=____mm . answer the question
Answer:
600
Step-by-step explanation:
since 1m=1000mm
What is the period of the function y=tan (n/4(x-n/3)? 3 units 4 units 6 units 8 units
Answer:
8
Step-by-step explanation:
The function u given me is
[tex] \tan( \frac{\pi}{4} (x - \frac{\pi}{3} ) )[/tex]
The period of a function is represented by
[tex] \frac{2\pi}{ |b| } [/tex]
where b is the coefficient of the x variable.
The coefficient is pi/4 so
[tex] \frac{2\pi}{ \frac{\pi}{4} } = 8[/tex]
8 is the answer.
Answer: 4 units
Step-by-step explanation:
Help me plz snsnsns sn
Answer:
If the exponent is 0 the answer is 224/y^2
Step-by-step explanation:
Solve each equation V/8=13
Answer:
v = 114Step-by-step explanation:
[tex] \frac{v}{8} = 13[/tex]
=> v = 13 × 8
=> v = 114 (Ans)
Use a real number to represent the situation.
The temperature falls 14°F.
Answer:
-14°F
Step-by-step explanation:
Hey there!
multiply : (5x+3a) (5x-3a)
Please help me
Find this value
Answer:
<CAB =30°
Step-by-step explanation:
<DAB=80°
<DAC=50°
<DAB=<DAC+<CAB
<CAB=<DAB-<DAC
=80°-50°
=30°
c) Convert 120 into quinary equivalent.
Assuming 120 is a base 10 numeral, then
120 = 100 + 20 = 4×5² + 4×5¹
so you have
120₁₀ = 440₅
Help me pls i have to finish my homework i have more questions to post too
Answer:
17) 19
19) 8
Step-by-step explanation:
17)
(6 +6² -4)÷2
(6 +36 -4)÷2
(38)÷2
19
19)
3³ ÷3 - 1
27 ÷3 -1
9 -1
8
Express each mixed number as a percent 2 1/2 can someone please tell me the awnser
Answer:
im pretty sure its 250%
Step-by-step explanation:
Answer:
250%
Step-by-step explanation:
1 is 100% and double that is 200%
1/5 of 100% is 50%
200% + 50% = 250%
Subtract.
5/23 - 4/23
(Type an integer or fraction.)
Answer:
1/23
Step-by-step explanation:
5/23 - 4/23 would be 1/23. When the denominators of the fractions are the same, you can just subtract the numerators.
) P is a set of prime numbers --- State it’s type.
A) Null set B) singleton set C) infinite set
E) A,B,C are correct.
Answer:
null set
Step-by-step explanation:
i am not sure but i hope it will help you
Answer:
singleton set is correct
suppose the two vertical angles are measuring 6x + 15 and 4x + 32. what is the measure of each angle?
Answer:
measure of both angle is 66
Step-by-step explanation:
vertical angles are equal so,
6x+15=4x+32
6x-4x=32-15
2x= 17
X=8.5
now,
4X+32
= 4×8.5 +32
= 66
Find the orthogonal decomposition of vector b = 9, 0, 0 with respect to vector a = 4, −5, 0 . (Your instructors prefer angle bracket notation < > for vectors.)
The orthogonal decomposition of vector [tex]\vec b = <9, 0, 0>[/tex] with respect to vector [tex]\vec a = <4, -5, 0>[/tex] is
[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]
From the Question we are told that
Vector [tex]\vec b = <9, 0, 0>[/tex]
Vector [tex]\vec a = <4, -5, 0>[/tex]
Generally in the orthogonal decomposition of b to a we have
[tex]\vec b=\vec b"+\vec b'[/tex]
Where
[tex]\vec b"=(\frac{\vec b*\vec a}{\vec *\vec a})*\vec a[/tex]
[tex]\vec b"=(\frac{ <9, 0, 0>*<4, -5, 0>}{<4, -5, 0>*<4, -5, 0>})*<4, -5, 0>[/tex]
[tex]\vec b"=<\frac{4}{5},\frac{-8}{5},0>[/tex]
Therefore
[tex]b'= \vec b- \vec b"\\\\b'=<4,0,0>-<\frac{4}{5},\frac{-8}{5},0>[/tex]
[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]
in Conclusion
The orthogonal decomposition of vector [tex]\vec b = <9, 0, 0>[/tex] with respect to vector [tex]\vec a = <4, -5, 0>[/tex] is
[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]
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You are trying to make a hole in one on the miniature golf green
3
3
5
7
9 X
a. Write an absolute value function that represents the path of the golf ball.
3
$ (z) = – 31x/+6
b. Write the function in part (a) as a piecewise function.
f(x) =
if x < 6
if x26
can someone please give me an example of a position and motion of objects in space
Answer:
position of objects in space
for example: up, down, in front, behind, between, left, right.
motion of objects in space
for example: Stars, planets, moons.
s= zh - 2zt^3 solve for z
Hi ;-)
[tex]s=zh-2zt^3\\\\z(h-2t^3)=s \ \ /:(h-2t^3)\\\\z=\dfrac{s}{h-2t^3}[/tex]
Answer:
z = [tex]\frac{s}{h-2t^3}[/tex]
Step-by-step explanation:
Given
s = zh - 2zt³ ← factor out z from each term
s = z(h - 2t³ ) ← divide both sides by h - 2t³
[tex]\frac{s}{h-2t^3}[/tex] = z
if n=4 and m=3 find 2n-3m
Answer:
hope it helps you........
Answer:
2n-3m
=2(4)-3(3)
=8 - 9
= -1
Which of the following represents the relationship
between h and C ?
A) C = 5h
3
B) C = - +5
4
C= +5
C) C = 3h + 5
D) h = 3C
Answer:
I think its c I hope I'm right
In x² , what is the 2 called?
a radical
a subscript
an exponent
an imaginary number
none of these
Answer:
an exponentStep-by-step explanation:
In x², here the 2 is exponent while x is base.
Answer:
an exponent
Step-by-step explanation:
hope it helps:)
What is the area of the figure?
A. 22 m2
B. 30 m2
O C. 33 m²
O D. 42 m2
E. 50 m2
Answer:
B. 30m2
Hope it helps you..slope 1/6 , x-intercept at -1
Answer:
[tex]{ \underline{ \sf{6y = x + 1 }}}[/tex]
Step-by-step explanation:
[tex]y = mx + c[/tex]
m is slope
c is y intercept.
at x-intercept, y = 0
[tex]0 =( \frac{1}{6} \times - 1 )+ c \\ \\ c = \frac{1}{6} [/tex]
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the given line is 6y=x+1.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Given that the slope of the equation of the line is 1/6, while the x-intercept is at -1. Therefore, if we substitute the coordinate of the intercept and the slope in the equation in the general equation of the line. We will see,
y = mx + c
0 = (1/6)(-1) + c
0 = -1/6 + c
c = 1/6
Now, the equation of the line can be written as,
y = (1/6)x + (1/6)
y = (x/6) + (1/6)
y = (x+1)/6
6y = x + 1
Hence, the equation of the given line is 6y=x+1.
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*Plz it due today HELP!!!!!!Justin has been collecting baseball cards for years. He bought 137 cards the first year
and 143 cards the second year. He plans on putting them in a binder that will hold seven
cards per page. How many pages must the binder have to hold Justin's collection? *Plz tell me what the math action word is I need to box it*
Answer:
40
Step-by-step explanation:
137+143=280
280/7= 40
Answer:
Division/dividing/divide
Step-by-step explanation:
If Justin has 280 baseball cards, and if each page will only hold 7 cards per page, then by dividing 280 by 7 (280÷7) would equal to 40 pages.
Guys help me in this question pls
Answer:
40+x+5 = 3x +15
2x= 30
x=15
Their present ages are 15 and 55
Geometry WS (Angle Addition Postulate) (20 pts)
Answer:
x = 17°
m∠MKL = 116°
m∠JKL = 159°
Step-by-step explanation:
JKM = 43
MKL = 8x - 20
JKL = 10x - 11
Since JKL is the whole angle, JKM + MKL = JKL
43 + 8x - 20 = 10x - 11
Add 20 to both sides:
43 + 8x = 10x + 9
Subtract 8x from both sides:
43 = 2x + 9
Subtract 9 from both sides:
34 = 2x
x = 17°
MKL = 8(17) - 20
MKL = 116°
JKL = 10(17) - 11
JKL = 159°
And to check 159 - 116 = 43
If my answer is incorrect, pls correct me!
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