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
Sladkaya [172]
3 years ago
13

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

Mathematics
1 answer:
charle [14.2K]3 years ago
8 0

ANSWER

See below

EXPLANATION

Given

f(x) =  \frac{ {x}- 9 }{x + 5}

and

g(x) =   \frac{ - 5x - 9}{x - 1}

(f \circ \: g)(x)=  \frac{ (\frac{ - 5x - 9}{x - 1})- 9 }{(\frac{ - 5x - 9}{x - 1} )+ 5}

(f \circ \: g)(x)=  \frac{ \frac{ - 5x - 9 - 9(x - 1)}{x - 1}}{\frac{ - 5x - 9 + 5(x - 1)}{x - 1} }

Expand:

(f \circ \: g)(x)=  \frac{ \frac{ - 5x - 9 - 9x  + 9}{x - 1}}{\frac{ - 5x - 9 + 5x - 5}{x - 1} }

(f \circ \: g)(x)=  \frac{ \frac{ - 5x - 9x  + 9 - 9}{x - 1}}{\frac{ - 5x + 5x - 5 - 9}{x - 1} }

(f \circ \: g)(x)=  \frac{ \frac{ - 14x }{x - 1}}{\frac{ -14}{x - 1} }

Since the denominators are the same, they will cancel out,

(f \circ \: g)(x)= \frac{ - 14x}{ - 14}  = x

You might be interested in
How can emily use the above to make an estimate for 576 ÷8
Grace [21]

Given the equation :

576\div8​

We will use estimation to find the value of the given expression

So, the best estimation for the number 576 is = 600

The best estimation for the number 8 is = 10

So, the given expression is approximately = 600 ÷ 10 = 60

===================================================================

We can calculate the error of the approximation as following :

The actual value is : 576 ÷ 8 = 72

So, the difference is = 72 - 60 = 12

so, the percentage of error will be :

\frac{12}{72}\cdot100=16.7\%

7 0
1 year ago
5) According to the histogram, how many shipments were received that had at most 30 bulbs broken? A) 4 B) 5 C) 9 D) 13
MariettaO [177]

Answer:

The answer would be A) 4

6 0
2 years ago
Death Valley headquarters in California is 190 feet below sea level. Badwater, America's lowest point, is 92 feet lower than Dea
olga_2 [115]

Answer: Badwater is 282 feet below the sea level.

Step-by-step explanation:

Given: Death Valley headquarters in California is 190 feet below sea level. Badwater, America's lowest point, is 92 feet lower than Death Valley headquarters.

To find the depth of Badwater we need to add depth of Death Valley headquarters from sea level to the depth of Badwater from Death valley headquarters.

i.e. The Depth of Badwater from sea-level = 190 feet +92 feet

= 282 feet

Hence, Badwater is 282 feet below the sea level.

3 0
3 years ago
What are 6 whole numbers -3.5 and 5.5
Blababa [14]

Answer:

This is    a long    long title      restart

3 0
3 years ago
Graph the data in the table. Which kind of function best models the data? Write an equation to model the data. quadratic; y = 2.
Oksanka [162]

Answer:

Option (1)

Step-by-step explanation:

x               -2              -1                 0                    1                   2

y               10            2.5                0                  2.5                3.0

Ist difference,

d_1=y_2-y_1

    =2.5-10=-7.5

d_2=y_3-y_2

    =0-2.5

    = -2.5

d_3=y_4-y_3

    =2.5-0

    = 2.5

d_4=y_5-y_4

    =10.0-2.5

    = 7.5

2nd difference,

x_1=d_2-d_1

    =-2.5+7.5

    = 5

x_2=d_3-d_2

    =2.5+2.5

    = 5

x_3=d_4-d_3

    =7.5-2.5

    = 5

Since 2nd difference is common, given table represents a quadratic equation.

Let the equation is,

y = ax²+ bx + c

For a point (0, 0) passing through the quadratic equation,

0 = c

Therefore, quadratic equation is y = ax² + bx

Since ordered pair (-1, 2.5) passes through the graph of the function,

2.5 = a(-1)² + b(-1)

a - b = 2.5 ------(1)

For another point (1, 2.5)

2.5 = a(1)² + b(1)

a + b = 2.5 ------(2)

By adding equations (1) and (2),

2a = 5

a = 2.5

and from equation (2)→ y = 0

Therefore, equation of the quadratic function given in the table is y = 2.5x²

Option (1) is the answer.

8 0
3 years ago
Other questions:
  • Two negative integers are 5 units apart on the number line, and their product is 126. What is the sum of the two integers?
    9·1 answer
  • (2 fiths) to the -2nd power btw, how can i use the camra in this app
    14·1 answer
  • Jasmine is making a quilt.
    8·1 answer
  • What are the perfect numbers between 1 and 28?
    8·1 answer
  • Please help ( question 9)<br> tyyyyy
    6·1 answer
  • Solve the cube root of x^2-8=2
    5·2 answers
  • 6/9×4/7 WHOEVER ANSWERS IN UNDER 2 MINUTS I WILL MARK BRAINLIEST
    13·2 answers
  • Carla has a store that sell candles for 4 for 10 dollars. A customer called and Carla needs to know how much 20 candles would co
    11·1 answer
  • ILL BRAINLIEST YOU PLEASE HELP ME
    6·1 answer
  • Input Output<br> 6<br> 0<br> 3<br> 6<br> 2<br> 12<br> Oy
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!