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
Solve the equation.
3(2x + 7) = - 23 + 14
Answers
Step-by-step explanation:
6x+21=-9
6x=-9-21
x=-30/6
x= -5
Answer:
[tex]3(2x + 7) = - 23 + 14 \\ 6x + 21 = - 9 \\ 6x = - 30 \\ x = \frac{ - 30}{6} \\ x = 5 \\ thnk \: you[/tex]
What is (f - g)(x)? f(x) = 3x g(x) = -3x² + 3x Write your answer as a polynomial or a rational function in simplest form.
Answers
Answer:
3x²
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x - (- 3x² + 3x) ← distribute parenthesis by - 1
= 3x + 3x² - 3x ← collect like terms
= 3x²
How do I write 125,740,689 in expanded form and in words
Answers
100,000,000 + 20,000,000 + 5,000,000 + 700,000 + 40,000 + 600 + 80 + 9
One hundred twenty five million, seven hundred forty thousand six hundred eighty nine
Step-by-step explanation:
cos5xcosx-sin5xsinx=??????????????????
Answers
Answer:
cos6x.
Step-by-step explanation:
We use the identity
cosAcosB - sinAsinB = cos(A+B)
so cos5xcosx - sin5xsinx = cos(5x + x)
= cos6x.
−5x+4y=3
x=2y−15
what would be the values of x and y
Answers
Answer:
x=9 y=12
Step-by-step explanation:
eqn 1 - x=2y-15
eqn 2- -5x+4y=3
-5(2y-15)+4y=3
-10y+75+4y-3=0
-6y+72=0
y= 12
x=2y-15
x=2(12)-15
x= 9
Substitution,
-5(2y-15) + 4y=3
-10y + 75+ 4y=3
75-3 = 10y - 4y
6y = 72
y. = 72/6
Y= 12
Now find x
X= 2(12) - 15
X= 24 - 15
X= 9
Soo
X= 9; Y= 12
Find the value of x (trig)
Answers
According to the figure:-
P=13H=25We know that Sin∅=P/H
Hence Sinx°=13/25
[tex] { \sin}^{ - 1} \frac{25}{13} = X°[/tex]
Be brainlyHelp please and thank you (Algebra 1)
Answers
Hi ;-)
[tex](-7x^3+9x^2-3)\cdot(-2x^2-5x+6)=\\\\=14x^5+35x^4-46x^3-18x^4-45x^3+54x^2+6x^2+15x-18=\\\\=\boxed{14x^5+17x^4-91x^3+60x^2+15x-18}[/tex]
ken has 5 lemons and 3 oranges in his shopping trolley and the cost of the fruit is $3.50. Barbie, with 2 lemons and 4 oranges pays $2. 10 for her fruit. how much does each type of fruit cost?
Answers
Answer:
A) 5 L + 3 O = 3.50
B) 2 L + 4 O = 2.10
Multiplying B) by -2.5
B) -5L -10 O = -5.25 then a adding A)
A) 5L + 3 O = 3.50
-7 O = -1.75
Oranges = .25 each
Lemons = .55 each
Step-by-step explanation:
Find the smallest number which is when divided by 25,30and75 leavrs remainder.
Answers
Answer
you cant have a remainder bigger then your divident
Step-by-step explanation:
Answer:
The Lowest common multiple of 25, 30 and 75 is 150.
Compute each of the following values for f (x) = 1/x-2. Step by step
a. f(2.5)
b. f(1.75)
c. f (2)
d. Justify your answer for part (C).
Answers
Step-by-step explanation:
subtitle values of x one by one:
a)f(2.5)=1/2.5-2
f(2.5)=1/0.5
f(2.5)=2
b)Now x=1.75
f(1.75)=1/1.75-2
f(1.75)=1/-0.25
f(1.75)=-4
c)x=2
f(2)=1/2-2
f(2)=1/0
f(2)=infinity
d)something divided by zero is equal to infinity that is exteremly large value
Use objects or shapes to describe a a right angle
Answers
Answer:
square because it has 4 90⁰ angles
Twice a number is forty in equation form
Answers
Answer:
2x = 40
Step-by-step explanation:
Let the number be x
Twice means 2 time
2 × x
2x
The product is 40
2x = 40
Step-by-step explanation:
Twice a number is forty
Let the number be x, then
2×x=40
2x=40
x=40/2
x=20
order from least to greatest 4^2,√15 ,-5/2,-2 1/3,1/16
Answers
Answer:
-2 1/3, 1/16, √15, 4^2
Following order from least to greatest.
4 The equation 5W + 3 = 4w + 9 is modeled below. w W 1 W W 1 1 W 1 1 W W 1 1 1 What value of w makes this equation true? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. MI - SI – PSA- S-
Answers
Answer:
w = 6.
Step-by-step explanation:
5w + 3 = 4w + 9
5w - 4w = 9 - 3
w = 6
Then, check your work!
5(6) + 3 = 4(6) + 9
30 + 3 = 24 + 9
33 = 33
So, w = 6 will be the correct answer.
Hope this helps!
Vie sold 45 raffle ticket. his brother sold twice as many. How many tickets did the sell together?
Answers
Answer:
135 tickets
Step-by-step explanation:
Vie's brother sold twice as many as Vie. So we multiply Vie's tickets by 2 to get the brother's.
VIe's brother sold 45 * 2 = 90 tickets
And all together the two sold
45 + 90 = 135 tickets
Evaluate the expression for x = -3 and y = - 4.
2x+2y=__.
Answers
Answer:
-14
Step-by-step explanation:
Substitute the values for the variables.
[tex]2(-3)+2(-4)\\-6-8\\-14[/tex]
Answer:
-14
Step-by-step explanation:
cause you do 2(-3) + 2(-4) = -14
At a competition with 7 runners, medals are awarded for first, second, and
third places. Each of the 3 medals is different. How many ways are there to
award the medals?
Decide if this is a permutation or a combination, and find the number of ways
to award the medals.
Answers
Answer:
35 different combinations
Step-by-step explanation:
This would be a combination because the same person cannot get all three medals so permutation is not the correct way to calculate this. We use the formula C(n,r)=(nr)=n!(r!(n−r)!)=? where n is the number of total objects and r is the number of objects taken from the total.
brainliest pls . . . uwu
MARKING BRAINLIEST !! using the distance formula falculate the perimeter of the triangle below
a. 27.9 units
b. 24.3 units
c. 25.7 units
d. 28.2 units
Answers
Answer:
a
Step-by-step explanation:
i didn't use the distance formula, instead i used the pythagrean theorum. i counted the units for the legs, and made three smaller triangle and solved them to find the lengths of the hypotenuse and the added the three of those together to find the perimiter of the original triangle
A studio charges a sitting fee of 25$ plus 7$ per each portrait sheet ordered. Write an expression that can be used to find the total cost to have photographs taken. Then the cost of purchasing twelve portrait sheets.
Answers
Hi
let's call X number of photo ordered.
So total Cost is C(x) = 7X+ 25
Il let you calculate for X = 12 . Have fun
Anyone know the answer?
Answers
Answer:
Step-by-step explanation:
(21 + 3y) + y = 90
21 + 4y = 90
4y = 69
y = 17.25
x = 21 + 3(17.25)
x = 21 + 51.75
x = 72.75
Answer check:
72.75 + 17.25 = 90
90 = 90 Corrrrrrect !
Explanation:
x = 3y + 21
And x + y = 90° (complementary angle)
Substitute x value in the equation:
3y + 21 + y = 90
4y + 21 = 90
4y = 69
y = 69/4
y = 17.25
x = 3(17.25) + 21
x = 51.75 + 21
x = 72.75
HELP
Write one equation that has solutions of x = -3 and x = 2.
Answers
Answer:
x = -3
Equation: 2x + 2 = -4
x = 2
Equation: 3x - 3 = 3
What is -0.56 as a fraction in simplest form?
-14/25
-5/6
-56/100
-7/10
Answers
Find the sum of 2√5 AND 4√3 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Answers
Answer:
hey why you delete my answers
Mr. Mad Scientist earns $152, 200 per year. If he has to pay 15% in Income taxes per year how much money does he have after he pays his taxes for the year? *
Answers
Answer:
he have after he pays his taxes for a year 152185
Help ASAP I’ll mark you as brainlister
Answers
Answer:
the range is from 6 to -4 (both inclusive)
Step-by-step explanation:
the domain is all values of x for which the function is defined and the range is all values of y for which the function is defined hence the domain is -3 to -11 and the range is 6 to -4
6.
For which discriminant is the graph possible?
A. b2 – 4ac = 7
B. b2 – 4ac = 0
C. b2 – 4ac = –12
Answers
Answer:
A. b2 – 4ac = 7
Step-by-step explanation:
Use Distributive property to write the expression without parentheses
Answers
Answer:
-4x + 5y
Step-by-step explanation:
-1/6 x 24 x simplifies to -1 times 4x, which is -4x. -1/6 times -30y simplifies to -1 times -5y, which is 5y.
-4x + 5y
Explanation:
- 1/6(24x - 30y) =
-4x + 5y
Multiply - 1/6 by the numbers in parentheses
I dont get how to do this please help me
solve for the absolute value equation show your work
Answers
Step-by-step explanation:
5.
[tex] | \frac{x}{3} +{ \frac{2}{5} } | = 2[/tex]
[tex] \frac{x}{3} = \frac{6}{5} [/tex]
[tex]5x = 18[/tex]
[tex]x = \frac{18}{5} [/tex]
and
x/3=-12/5
x=-36/5
Kim is making cookies. She is using a recipe that calls for 1/4 cup of lemon juice. She has a 6 fl oz. bottle of lemon juice. There are 8 fl oz. of lemon juice in 1 cup. How many batches of cookies can she make?
Answers
Answer:
3
Step-by-step explanation:
Answer:
Step-by-step explanation:
1 cup = 8 fl oz
x cup = 6 fl oz Cross multiply
6 oz * 1 cup = 8 oz x divide by 8
x = 6 oz /8 oz = 3/4 cup
If kim needs 1/4 cup per batch then she will have enough for 3 batches of 1/4 cup each.
[tex]\tt\huge\red{Please \: help \: me!}[/tex]
Answers
First find Divisor
Two zeros are -3,-2[tex]\\ \sf\longmapsto x^2-(-3-2)+(-3)(-2)[/tex]
[tex]\\ \sf\longmapsto x^2+5x+6[/tex]
Dividend given by
[tex]\\ \sf\longmapsto x^4-x^3-16x^2+4x+48[/tex]
We know
[tex]\boxed{\sf Dividend=Divisor\times Quotient +Remainder}[/tex]
Remainder is 0[tex]\\ \sf\longmapsto Dividend=Divisor\times Quotient[/tex]
[tex]\\ \sf\longmapsto Quotient=\dfrac{Dividend}{Divisor}[/tex]
[tex]\\ \sf\longmapsto \dfrac{x^4-x^3-16x^2+4x+48}{x^2+5x+6}[/tex]
[tex]\\ \sf\longmapsto x^2-6x+8[/tex]
Now factor
[tex]\\ \sf\longmapsto x^2-6x+8=0[/tex]
[tex]\\ \sf\longmapsto x^2-4x-2x+8=0[/tex]
[tex]\\ \sf\longmapsto x(x-4)-2(x-4)=0[/tex]
[tex]\\ \sf\longmapsto (x-4)(x-2)=0[/tex]
[tex]\\ \sf\longmapsto x-4=0\:or\:x-2=0[/tex]
[tex]\\ \sf\longmapsto x=4\:or\:x=2[/tex]
Hence all zeros are
2,-2,-3,4