1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tems11 [23]
3 years ago
13

State of the given functions are inverses

Mathematics
1 answer:
bonufazy [111]3 years ago
3 0

Answer:

1) They are not inverses

2) They are inverses

Step-by-step explanation:

We need to find the composition function between these functions to verify if these functions are inverses. If f[g(x)] and g[f(x)] are equal to x they are inverses.

<u>1)</u>

<u>Let's find f[g(x)] and simplify.</u>

f[g(x)]=\frac{1}{2}g(x)+\frac{3}{2}

f[g(x)]=\frac{1}{2}(4-\frac{3}{2}x)+\frac{3}{2}    

f[g(x)]=\frac{7}{2}-\frac{3}{4}x

As f[g(x)] is not equal to x, these functions are not inverses.

2)

<u>Let's find f[g(x)] and simplify.</u>

f[g(n)]=\frac{-16+(4n+16)}{4}

f[g(n)]=\frac{-16+4n+16}{4}

f[g(n)]=\frac{4n}{4}

f[g(n)]=n

Now, we need to find the other composition function g[f(x)]

<u>Let's find g[f(x)] and simplify.</u>

g[f(x)]=4(\frac{-16+n}{4})+16

g[f(x)]=-16+n+16

g[f(x)]=n

Therefore, as f[g(n)] = g[f(n)] = n, both functions are inverses.

I hope it helps you!  

You might be interested in
Scott buys candy that costs $8 per pound. He will buy at least 5 pounds of candy. What are the possible amounts he will spend on
Dmitry_Shevchenko [17]

Answer: 8*5≥c  

sorry if wrong! Not my strong suit !

6 0
3 years ago
what is the volume of a rectangular prism that has a length of 8.5 centimeters (cm), a width of 3.2 centimeters, and a height of
Yuki888 [10]

Answer:

The volume of the rectangular prism is 163.2cm^3

Step-by-step explanation:

A rectangular prism is in the shape of cuboid which has three dimensions i.e Length, width and height.

Given: Length =8.5 cm width= 3.2 cm  and Height= 6 cm

The volume of a Cuboid = Length*Width*Height

Applying the given dimensions in the formula:

   

          The volume of a Cuboid=  8.5cm*3.2cm*6cm

                                               =  163.2cm^3

The volume of the rectangular prism is 163.2cm^3

3 0
3 years ago
A truck weighs 5400 lb in Open Wheel race car weighs 1/4 as much how much does the race car weigh
kap26 [50]
1,350 pounds

.........
4 0
3 years ago
Read 2 more answers
Are the graphs of 6 <br>y = -2x + 4 and y = 6x - 4 parallel perpendicular or neither
timurjin [86]
1st slope is -1/3. 2nd slope is 6

slope is same in parallel lines so not parallel

slopes are negative reciprocals in perpendicular lines so they aren't perpendicular

they are called oblique
4 0
3 years ago
Determine the slope of the lines.
JulijaS [17]
i think it’s perpendicular
7 0
3 years ago
Other questions:
  • On march 12, klein company, inc. sold merchandise in the amount of $7,800 to babson company, with credit terms of 2/10, n/30. th
    9·1 answer
  • The area of Nathan's bedroom rug is 15 square feet.The longer side measures 5 feet. His living room rug is twice as long and twi
    10·1 answer
  • Can someone help me out (image bellow)
    7·1 answer
  • Given 7, 9, and 11 as the three sides of a triangle, classify it as one of the
    11·1 answer
  • Because the length cannot be negative the height of the plane is ___ miles.
    13·1 answer
  • Solve n – 96 &lt; –58.
    12·1 answer
  • Does anyone know the answer to these questions???
    12·2 answers
  • at a certain fast-food restaurant, the volume of a large soda is 35% greater than the volume of a small soda. if the volume of t
    14·1 answer
  • Select all of the numbers that are irrational.
    5·2 answers
  • What is the range of the function graphed below?<br><br>I REALLY NEED HELPP!!​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!