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Greeley [361]
3 years ago
7

What is the inverse of the function f(x) = 2x + 1?

Mathematics
1 answer:
aliina [53]3 years ago
5 0
First, conceptually understand what an inverse function is, it makes solving it very intuitive.  An inverse function is simply a function which has points (y,x) for every point (x,y) of the parent function.  So you are essentially taking all points of the parent function and switching the x and y coordinates for each.  Those switched coordinates are produced by the "inverse function".

Mathematically then, finding the inverse function is a matter of solving for x and then switching the variable labels.  In this case:

y=2x+1  subtract 1 from both sides

y-1=2x  divide both sides by 2

(y-1)/2=x  now just switch the labels for the variables...

y=(x-1)/2  so

f^-1(x)=(x-1)/2  is the inverse of f(x)=2x+1
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Jenna saves $3 for every $13 she earns. Vanessa saves $6 for every $16 she earns. Is Jenna’s ratio of money saved to money earne
Alexxx [7]

Answer:

3/13 and 6/16

Step-by-step explanation:

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7 0
3 years ago
Below is a drawing of a wall that is to be covered with either wallpaper or paint. The wall is 8 ft. high and
Snowcat [4.5K]

84 sq. ft of the wall has to be covered with paint or wallpaper.

Step-by-step explanation:

  • Step 1: Find the area of wallpaper to be covered by calculating the area of the wall and subtracting the areas of the window, mirror and fireplace from it. All are rectangular in shape with are given by A = length × width

Area of the wall = 8 × 16 = 128 ft²

Area of the window = 18/12 × 14 = 1.5 × 14 = 21 ft² (since 1 ft = 12 in)

Area of the fireplace = 5 × 3 = 15 ft²

Area of the mirror = 4 × 2 = 8 ft²

  • Step 2: Calculate the area to be painted or covered with wallpaper

Area of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)

                              = 128 - 44

                              = 84 ft²

5 0
3 years ago
Read 2 more answers
F(x)=2.8x-12 and g(x)=5.8x+9
xxMikexx [17]
Hi, there! 

I'm not sure what you want to solve in these equations. Please provide me with more details. I am sorry if you were looking for answers to the question, but I simply do not know what you are asking for. 

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6 0
3 years ago
Solve for the given variable. Record your work and check the solution, if possible.
nikdorinn [45]

Answer:

10

Step-by-step explanation:

75c-300=25c+200

-25c         -25c

50c-300=200

+300         +300

50c=500

c=10

4 0
3 years ago
Read 2 more answers
1. (10pts] Let A = {1, 2, 3, 4, 5}, let B = {1,4,5,7,8,9}, and let C = {2, 4, 6, 7,9}. Determine each of the following (a) An Bn
alisha [4.7K]

Answer and explanation:

Given : Let A = {1, 2, 3, 4, 5}, let B = {1,4,5,7,8,9}, and let C = {2, 4, 6, 7,9}.

To find : Determine each of the following,

a) (A\cap B)\cap C

b) (A\cup B)\cap (A\cup C)

c) A - (B\cup C)

d) (A-C) (C-A)

Solution :

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets.

The intersection of two sets is a new set that contains all of the elements that are in both sets.

a) (A\cap B)\cap C

A\cap B=\{1,4,5\}

Then, (A\cap B)\cap C=\{4\}

b) (A\cup B)\cap (A\cup C)

A\cup B=\{1,2,3,4,5,7,8,9\}

A\cup C=\{1,2,3,4,5,7,9\}

(A\cup B)\cap (A\cup C)=\{1,2,3,4,5,7,9\}

c) A - (B\cup C)

B\cup C=\{1,2,4,5,6,7,8,9\}

A - (B\cup C)=\{3\}

d) (A-C) (C-A)

A-C=\{1,3,5\}

C-A=\{6,7,9\}

(A-C) (C-A)=\{1,3,5\}\times\{6,7,9\}

(A-C) (C-A)=\{(1,6),(1,7),(1,9),(3,6),(3,7),(3,9),(5,6),(5,7),(5,9)\}

5 0
3 years ago
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