Given that f(x)=2x+1
a) find f(2)
b)find f^-1(x)
c)f^-1(7)

Answers

Answer 1

Answer:

a) [tex]f(2) = 5[/tex], b) [tex]f^{-1} (x) = \frac{x-1}{2}[/tex], c) [tex]f^{-1} (7) = 3[/tex]

Step-by-step explanation:

a) We evaluate the function at [tex]x = 2[/tex]:

[tex]f(2) = 2\cdot (2) + 1[/tex]

[tex]f(2) = 4+1[/tex]

[tex]f(2) = 5[/tex]

b) First, we determine the inverse of the function by algebraic means:

1) [tex]y = 2\cdot x + 1[/tex] Given

2) [tex]y +(-1) = 2\cdot x + [1+(-1)][/tex] Compatibility with addition/Associative property

3) [tex]y + (-1) =2\cdot x[/tex] Existence of additive inverse/Modulative property

4) [tex]2^{-1}\cdot [y+(-1)] = (2\cdot 2^{-1})\cdot x[/tex] Compatibility with multiplication/Commutative and associative properties

5) [tex][y+(-1)]\cdot 2^{-1} = x[/tex] Existence of multiplicative inverse/Modulative and commutative properties

6) [tex]x = [y+(-1)]\cdot 2^{-1}[/tex] Symmetry property of equality

7) [tex]x = \frac{y-1}{2}[/tex] Definitions of subtraction and division

8) [tex]f^{-1} (x) = \frac{x-1}{2}[/tex] [tex]x = f_{-1} (x)[/tex]/[tex]y = x[/tex]/Result

c)  Now we evaluate the expression obtained on b) at the given number:

[tex]f^{-1} (7) = \frac{7-1}{2}[/tex]

[tex]f^{-1} (7) = 3[/tex]


Related Questions

n +-6 = 11
Please answer!

Answers

Answer:

n = 17

Step-by-step explanation:

+(-6) is the same thing as n - 6 = 11 to take out the + sign in order to avoid confusion.  Add 6 on both sides to get your n value which is 17.

Answer:

Step-by-step explanation:

here you go mate

step 1

n +-6 = 11  equation/Question

step 2

n +-6 = 11  add 6 to each side

n-6(+6)=11(+6)

answer

n=17

I need help please :'v​

Answers

Answer:

Slope = 2

Step-by-step explanation:

[tex]\frac{-8-8}{-6-2}=\frac{-16}{-8}=2[/tex]

Answer:

2

Step-by-step explanation:

using formula given y2-y1/x2-x18-(-8)/2-(-6)8+8/2+616/82

answers for the 2 boxes please ​

Answers

Answer:

(4,9)

Step-by-step explanation:

y = 2x + 1

y = x + 5

2x + 1 = x + 5

2x - x = 5 - 1

x = 4

y = x + 5

y = 4 + 5

y = 9

Check:

(4,9) ? Yep

Which solution shown below contains an error?
3
4
3x
4
3x+4
?
ਦੇਸ਼ ਦੇ
1
+2
2
x+2
1
x+1
+2
2
3
+
21-12
8x+8
(x+1)(x-6) * (x+1)(x-6)
+1
- 8
1px-4
(+1)(-6)

Answers

Answer:

B

Step-by-step explanation:

1/x+2 + 1/x+2 = 2/x+2 = 1/x+1.

Help !! Answer please

Answers

Answer:

4

Step-by-step explanation:

jan has a 12-ounce milkshake.Four ounces in the milkshake are vanilla,and the rest is chocolate.What are two equivalent fractions that represent the fraction of the milkshake that is vanilla

Answers

Answer:

In this item, we are given that out of 12 ounces of ingredients comprising the milkshake, there are 4 ounces vanilla. Expressing this into fraction will give us an answer of 4/12. This fraction can be one of the answers. Since we are asked for two fractions, we can simplify 4/12 such that we get an equivalent fraction that is equal to 2/6. Hence, the answers to this question are 4/12 and 2/6.

Step-by-step explanation:

A rectangle is 2 times longer than it is wide. The diagonal of the rectangle is 15 cm. What is the width of the
rectangle?

Answers

This is fairly simple. Just do 2x15 to get your answer 2x15=30. Explanation if it is 2 times longer you would do 2 and then when it says it is 15 diagonal that is where the 15 comes in and it would be 2x15. So your answer is 30
Your answer would be 30

The table below shows the temperature changes
Monday morning in Bedford, New York over a 4-hour
period after a cold front came through.
a. If the beginning temperature was -10°F at 5:00 a.m.,
what was the temperature at 9:00 a.m.?

Answers

It is going to be the last one question

20\left(-1.5r+0.75\right)20(−1.5r+0.75)20, left parenthesis, minus, 1, point, 5, r, plus, 0, point, 75, right parenthesis

Answers

Answer:

wet

Step-by-step explanation:

fart

Answer:

3.25

Step-by-step explanation:

did on khan

Solve This Proportion Y/23= -3/4 ​

Answers

Answer:

y = -17.25

Step-by-step explanation:

y/23 = -3/4

by cross multiplication ;;;

4×Y = 23× (-3)

4y = (-69)

y = -69/4

y = -17.25

I hope that this answer helps you

what is the value of k used to find the coordinates of a point that partitions segment into ratio 5:3?

Answers

Answer:

(5+3 = 8)

Step-by-step explanation:

The value of k is found by dividing the numerator of the original ratio, 5, by the sum of the numerator and denominator of the ratio (5+3 = 8).

I really need help please!

Answers

...............................
12 of them said that they prefer Coca Cola but the pupils all together said that they prefer milk on it.

3.75x-5-8.75X+4.5+0.5

Answers

Step-by-step explanation:

3.75x-5-8.75x+4.5+0.5

=3.75x-8.75x+4.5+0.5-5

=-5x+5-5

==-5x

14 x 18. How do you do distributive property?

Answers

The answer is:14x18= 252

OK!!! I NEED HELP AGAIN AND ITS HONESTLY SUPER EASY :/ I DONT KNOW WHY IM NOT doing it BY MYSELF BUTTTTT---- GIVING BRAINLIEST, FIVE STARS AND THANKSSS!

Which measurement is most accurate to describe the amount of water a bucket could hold?

3 gallons
5 pints
30 fl. oz.
10 cups

Answers

Answer:

3 gallons

Step-by-step explanation:

Please help ASAP!!
The question is attached ​

Answers

The correct chain is A.

Answer: A

3/4 equals 6/8 and 9/12 and 12/16

could someone please help me with this​

Answers

Answer:

E is the correct choice

Step-by-step explanation:

i hope this helps

Math PLS (I'll try to give brainlest)

Answers

Answer: The function is non-linear. Linear functions need to be straight

What are the leading coefficient and degree of the polynomial?
- 4x - 10x +3 - 10x2

Answers

Answer:

10x^2-4x-10x+3

leading C is 10

D is 2

Step-by-step explanation:

HELPPPPPPPPPPPPPPPPPP

Answers

Answer:

The answer to this d=0.6t because evry minute it is .6

for what value of x is d parallel to e?
A) 20
B) 25
C) 35
D) 37

Answers

7x+3+2x-3 = 180
9x = 180
X= 20
A is the answer
I’m pretty sure It’s A
Hope this helps! Have a great day ^W*

Arjun's piggy bank contains two kinds of coins and two kinds of bills. there are twice as many $1 bills like $5 bills. the number of quarters is 1 more than three times the number of $5 bills. and the number of dimes is 7 less than the number of quarters. how many of each type of bill and coin does Arjun have if the total is $39.90?

Answers

Answer:

$5 bills x 5, $1 bills x 10, quarters x 16, dimes x 9

Step-by-step explanation:

$5 bills = x, total = 5x$1 bills = 2x, total = xQuarters = 3x + 1, total = 0.25(3x + 1)Dimes = 3x + 1 - 7= 3x - 6, total = 0.1(3x - 6)

Equation below as the sum, solve for x:

5x + 2x + 0.25(3x + 1) + 0.1(3x - 6) = 39.97x + 0.75x + 0.25 + 0.3x - 0.6 = 39.98.05x  - 0.35 = 39.98.05x = 40.25x = 40.25/8.05x = 5

Number of each bill and coin:

$5 bills = 5$1 bills = 2*5 = 10Quarters = 3*5 + 1 = 16Dimes = 3*5 - 6 = 9

(-3, -7). 1/7 what is the equation in point slope form

Answers

Answer:

y+7 = 1/7(x+3)

Step-by-step explanation:

Point slope form of a line is given by

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

(y -  -7) = 1/7(x - -3)

y+7 = 1/7(x+3)

Solve for x in the following equation
2^(8x-8)=4^7x

Answers

Answer:

-4/3

Step-by-step explanation:

2^(8x-8)=4^7x

2^8x-8=4^7x

2^8x-8=4^2×7x

8x-8=2×7x

8x-8=14x

-8=14x-8x

-8=6x

-8/6=x

-4/3=x

x=-4/3

This recipe makes 10 portions of porridge.
Complete the amount of each ingredient that is needed to make just 7 portions.

Recipe: Serves 10
350 g oats
1.4 l milk
70 g sugar

PLEASE HELPP

Answers

Answer:

245g oats

0.98L milk

49g sugar

Step-by-step explanation:

350÷10=35

1.4÷10=0.14

70÷10=7

35×7=245

0.14×7=0.98

7×7=49

how do i find an equation for a line with an x-intercept of 4 and a y-intercept of -2

Answers

Answer:

The equation of a line is y = ax + b, where a is the slope and b is the y-intercept.  

Since we have the y-intercept, all we need to do is find the slope. To find the slope, you need 2 coordinates.

The y-intercept is where the line crosses the y axis, so it is where x is 0. Since the y intercept is -2, that means the first coordinate is (0, -2)

The x-intercept is where the line crosses the x axis, so it is where y is 0. Since the x intercept is 4, that means the second coordinate is (4, 0)

Since we already have the y-intercept, all we do is put the slope in the equation: y = 1/2x - 2.

Step-by-step explanation:

err i dont know U>U here you go peeps

Answers

Answer:

[tex] {x}^{2} + {y}^{2} + 4x - 2y = - 1 \\ ( {x}^{2}+2\times2\times x + {2}^{2} ) - 4 + ({y}^{2} - 2 \times 1 \times y + {1}^{2} ) - 1 = - 1 \\ {(x + 2)}^{2} - 4 + {(y - 1)}^{2} - 1 = - 1 \\ {(x + 2)}^{2} + {(y - 1)}^{2} = 4\\ {(x + 2)}^{2} + {(y - 1)}^{2} = {( 2) }^{2} [/tex]

Therefore, the centre of the circle is in ( -2, 1 )

and the radius of the circle is 2.

Formula used :-----

[tex] {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} [/tex]

equation of the circle

where r is the radius of the circle.

(A) 2 is the right answer.

5/7 x 14/20

Snannan

Answers

Answer:

[tex] \frac{1}{2} \: or \: 0.5 [/tex]

Step-by-step explanation:

[tex] \frac{5}{7} \times \frac{14}{20} = \frac{5 \times 14}{7 \times 20} [/tex]

It can be also written as -

[tex] = > \frac{5 \times 14}{20 \times 7} = \frac{5}{20} \times \frac{14}{7} = \frac{1}{4} \times 2 = \frac{1}{2} [/tex]

Can someone please help answer this question quickly? :)

Answers

8 because x + 8 =y Example : 18+8 = 26

Solve 24 ≤ -6t

The solution is ___

Graph the solution.

Answers

Answer:

T < - 4

Step-by-step explanation:

Answer:

t<-4

Step-by-step explanation:

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