Mathematics High School

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

Help !! Answer please

Answers

Answer:

4

Step-by-step explanation:

Someone pls help what would this slope be ?

Answers

Answer:

-3/5x

Step-by-step explanation:

It is a negative slope and use rise over run

====MATH QUESTION====Extra points

Answers

I think the answer is A :) i hope this helps

please help with this.

Answers

Answer:

b

Step-by-step explanation:

Answer:

I think your answer is B.

Step-by-step explanation:

Not 100% sure though

HELP ASAP!!!!!!!

PLS I NEED THIS TURNED IN IN 10 MINS

Answers

Answer:

slope = 2

y-int = 3

Step-by-step explanation:

y-intercept can be determined by the coordinate (0,3) which is 3 units up from origin on the y-axis

slope can be determined by taking the difference of a pair of y-values and dividing it by the difference of the x-values

ex,  3 - 1    = 2

     0 - (-1)      1

or:   5 - 3  = 2

        1 - 0        1

4 Isabel is designing a new fish tank that is shaped like a triangular prism with lateral faces made of glass. A model of the fish tank and its dimensions are shown below. 10 in 8 in 1 6 in 8 in What is the lateral surface area of Isabel's fish tank? ​

Answers

Answer: 192 in2

AL=(a+b+c)h=(10+8+6)·8=192

In a system of two linear equations, the lines represented by each equation have the same slope. Which could be the total number of solutions to the system of equation

Answers

Answer:

Please see explanation

Step-by-step explanation:

A system of linear equations in two variables represents two lines on graph.

When both the lines have same slope, there can be two cases

Same slope with different y-intercepts

When two lines have same slope and different y-intercepts, that means that both lines are parallel and parallel lines have no solution.

Same slope with same y-intercepts

When the slope of both lines is same and the y-intercept is also same, this means that both the equations refer to the same line. This means that the system has infinite number of solutions.

How are the functions
f(x) = 16* and
19(x) = 161/2
related?

Answers

Answer:

F(x) = 16^x = 8^2x

g(x) = 16^1/2x = 8^x

So you can see the relationship. They are all of the type a^bx form, with same base of a, f(x) will have larger increasing rate.

Step-by-step explanation:

Ivan has 17 times as many nickels as Nicole.Select the variable expression that shows how many nickels Ivan has if n is the number of nickels that Nicole has.

Answers

Answer:

17 n

Step-by-step explanation:

Ivan has 17 times as many nickels as Nicole.

Let Nicole has n nickels.

It would mean that,

No. of nickels Ivan have = 17n

Hence, there are 17n nickels Ivan has.

Answer:

17n

Step-by-step explanation:

Here is a number line write down the inequality shown on the number line

Answers

Answer:

[tex] - 3 < x \leqslant 2[/tex]

Answer:

-3<p<2

Step-by-step explanation:

Pls help I’m bad at math no matter how much I try

Answers

Answer:

no it is not

Step-by-step explanation:

Ms. Petters has 36 red, blue, and green markers. She has an equal number of each color of marker. She arranges the red markers in 2 equal groups. How many red markers are in each group?​

Answers

The answer should 6 Ik for sure

What is the geometric mean of 7 and 56

Answers

19.7989898732 or to simplify it 19.79
19.79 is the answer to your question

The parabola in the figure below has an equation of the form
y = ax^2 + bx - 4.

Find the equation of the parabola

Answers

Answer:

y = - x² + 5x - 4

Step-by-step explanation:

Given that the zeros are x = 1 and x = 4 , then the corresponding factors are

(x - 1) and (x - 4) , then

y = a(x - 1)(x - 4) ← a is a multiplier

   = a(x² - 5x + 4)

To find a substitute the coordinates of any other point on the parabola into the equation.

Using (2, 2), then

2 = a(4 - 10 + 4) = - 2a ( divide both sides by - 2 )

a = - 1

Thus

y = - (x² - 5x + 4) = - x² + 5x - 4 ( with a = - 1 and b = 5 )

What is the value of x

Answers

Answer:

4.4

Step-by-step explanation:

10/4=2.5

11/2.5=4.4

What is the measure of an interior angle of a regular nonagon?

Answers

Each angle of a regular nonagon is of 140°. A nonagon in which all sides are not equal and all angles are not equal. The measure of it’s angles are different but total sum of all its interior angles is always 1260°.

Solving Multi-Step Equations Maze
Drag the appropriate arrow to
show your path as you go
from the start to the finisch
DOWN START ve cochojuan for Xbo v pollo heard
START
(2x + 1) - 36
5(x ) - 100
2.75
Jul
10
Jul
3(2x + 4) 19
182x-X-7
18-15-3(6x + 5)
15
Til hay
II
58 7x25 - 4
X-9.6x22.5
15
-6,3
THE
END

Answers

Hmmm ik it’s called the hot dog method

The cost to rent a truck is $75 flat fee, plus $0.55 per mile driven. The table below shows the total cost of the renting the truck for the first four miles.

Answers

Answer:

75+ 0.55x = total amount

75 + (0.55 X 60) = $108

Step-by-step explanation:

x is a variable and represents the number of miles you drive, since you drive 60 miles you should figure out how much is 60 miles then add the flat fee of 75

Carla and Andrew have 29 chocolate chip cookies. Andrew has 8 more than twice Carla’s cookies. How many cookies does each person have?

Answers

Step-by-step explanation:

29 cookies

Carla has X cookies

Andrew has 8+ 2X cookies

x + 8 + 2x = 29

3x = 29-8

3x= 21

x = 7 / Carla has 7 cookies

8+ 2x = 8+2•7= 8+14=22 / Andrew has 22 cookies

Gia opened two savings accounts at two diffrent banks. One account earns an annual 3.4% simple interest, and the other earns half as much. If she deposited $509 in each account, how much total interests will sh have earned in 3 years? A:$153.00 B:$38.25 C:$76.50 D:$51.00

Answers

Interest from first account is :

[tex]I_1 = \dfrac{p\times r \times t}{100}\\\\I_1 = \dfrac{509\times 3.4\times 3}{100}\\\\I_1 =\$ 51.918[/tex]

Interest form second account is :

[tex]I_2 = \dfrac{p\times r\times t}{100}\\\\I_2 = \dfrac{509\times 1.7\times 3}{100}\\\\I_2 = \$25.959[/tex]

So, total interest is :

[tex]I = I_1 + I_2 \\\\I = 51.918 + 25.959\\\\I = \$77.877[/tex]

Therefore, total interest is $77.877 .

Here is a list of numbers.
32 29 30 37 34 33 31 Work out the median

Answers

Answer:

20, 29, 30, 31, 32, 33, 34, 37

~ the median is: 31 +32 / 2 = 31.5

Step-by-step explanation:

29 27 25 23 21 19
Plz mark me as Brainly

ASAP PLEASE!!!

Graph the equation.
y-3 = -x + 4)

Answers

Answer:

i think the correct answer is letter D im not sure

Step-by-step explanation:

simplify the equations below

Answers

Answer:

Problem 1:  1/64x^8

Problem 2: y^8/9x^2

Step-by-step explanation:

In the first problem, you first need to multiply the -2 exponent to everything in the parenthesis. This is equal to 1/64x^4*-2, simplified to be 1/64x^-8. Finally you simplify the x to 1/64x^8.

For the second problem, you do the same in the first one, getting x^-2/9y^4*-2. This can be simplified to be 3x^-2/y^-8. Finally you make sure there is no negative exponents, so you do y^8/9x^2.

Answer:

1/64x^8 and y^8/9x^2

Step-by-step explanation:

hope this helps have a good night :)

please i need help as soon as possible

Answers

The equation of the line is y= -2x+10

First you need to find the slope of the two points.
The slope is -2

Then you use the slope intercept form to find the y intercept.
y=2x+b

You then have to plug in the x and y points.

6= -2(2) + b
6= -4+b
b=10

Lastly write using the slope intercept

y= -2x+10

Hope this helps <3

How much of the circle is shaded? Write your answer as a fraction in simplest form.
3/7 and 1/4

Answers

Answer: 19/28

Step-by-step explanation:

3/7 + 1/4

Find the LCM for 7 and 4

12/28 + 7/28 = 19/28

What is the correct equation to solve for x ?

Answers

x=15.96

x=17.6

x=11.81

x=12.23

Determine whether the given value of the variable is a solution to the inequality 3b + 2 < 14 when b = 4

Answers

Answer:

I dont think it that would be the solution because 14 has to be greater and not equal.

Step-by-step explanation:

3(b) + 2 < 14

3(4) + 2 < 14

12 + 2 < 14

14 < 14

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Answers

Answer:

ok and ty oof

Step-by-step explanation:

Which of the following equations , in it's simplest form , will be equivalent to 3x+2+(-5)?

A: 2+3x+5. B: x-1+x-2+x C: -3-3x-1+x
D: 3-3x

Answers

Answer:

The correct answer would be B: x-1+x-2+x

Step-by-step explanation:

First, you would do 2+(-5), from the given equation. Then, it could be simplified to 3x-3. Then, looking at B, you would add the like terms, meaning you would add all the x´s together, and the whole numbers together, giving you 3x-3. I hope I made this easy to understand for you!

I don't get it, the concept is to make a proof, but I'm so confused!!!!

Answers

Answer:

Try Finding What A And B Is...

Step-by-step explanation:

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