8,669 - (4,398 + 571) is this an equation

A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions u

Kryger [21]

Given: $f(x) = \frac{1}{x-2}$

$g(x) = \frac{2x+1}{x}$

A.)Consider

$f(g(x))= f(\frac{2x+1}{x} )$

$f(\frac{2x+1}{x} )=\frac{1}{(\frac{2x+1}{x})-2}$

$f(\frac{2x+1}{x} )=\frac{1}{\frac{2x+1-2x}{x}}$

$f(\frac{2x+1}{x} )=\frac{x}{1}$

$f(\frac{2x+1}{x} )=1$

Also,

$g(f(x))= g(\frac{1}{x-2} )$

$g(\frac{1}{x-2} )= \frac{2(\frac{1}{x-2}) +1 }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{\frac{2+x-2}{x-2} }{\frac{1}{x-2}}$

$g(\frac{1}{x-2} )= \frac{x }{1}$

$g(\frac{1}{x-2} )= x$

Since, $f(g(x))=g(f(x))=x$

Therefore, both functions are inverses of each other.

B.

For the Composition function $f(g(x)) = f(\frac{2x+1}{x} )=x$

Since, the function $f(g(x))$ is not defined for $x=0$ .

Therefore, the domain is $(-\infty,0)\cup(0,\infty)$

For the Composition function $g(f(x)) =g(\frac{1}{x-2} )=x$

Since, the function $g(f(x))$ is not defined for $x=2$ .

Therefore, the domain is $(-\infty,2)\cup(2,\infty)$

8 0

4 years ago

A number n plus 8 is greater than 11? What is the inequality and the solution?

fomenos

Answer:

n+8 > 11

subtract 8 from 11

n>3

7 0

3 years ago

Read 2 more answers

Find the area of the isosceles triangle.<br>13 cm<br>10 cm

insens350 [35]

Answer:

65 cm

Step-by-step explanation:

A= 1/2 bh

A= 1/2 (13 cm) (4 cm)

A= 65 cm

7 0

3 years ago

Read 2 more answers

I. Daska is situated at a distance of 15 miles from both Gujranwala and Sialkot. A bus travels from Gujranwala to Daska at an av

son4ous [18]

Answer:

The average speed of the entire trip is 8.5 miles per hour.

Step-by-step explanation:

Speed = Total Distance / Total Time

So we have to find the total distance and the total time taken .

1) From Gujranwala to Daska

speed= 25miles/hour distance = 15miles

Time taken = distance / speed

= 15/25= 0.6 hours

2) From Daska to Sialkot

speed= 40miles/hour distance = 15miles

Time taken = distance / speed

= 40/15= 2.67 hours

3 ) From Sialkot to Daska

speed= 30miles/hour distance = 15miles

Time taken = distance / speed

= 30/15= 2 hours

The total distance traveled to three places is = 15+ 15+15= 45miles

The Total time taken is = 0.6+ 2.67+ 2= 5.267=5.3 hours

Speed = Total Distance / Total Time

Speed= 45/ 5.3

= 8.49=8.5 miles per hour

The average speed of the entire trip is 8.5 miles per hour.

7 0

3 years ago

If natalie and her friends decide to rent 4 lanes at reguler cost for a party ten people need to rent shoes and 4 people are mem

taurus [48]

The question is missing a tabular data. So, it is attached below.

Answer:

The total cost for the party is $74.50.

Step-by-step explanation:

Given:

Lanes rented at regular cost = 4

Cost of 1 lane rented at regular cost = $9.75

Cost of 1 lane rented for members = $7.50

Cost of 1 shoe rental at regular cost(non members) = $3.95

Cost of 1 shoe rental for members = $2.95

Since, lanes are rented at regular cost, we use unit rate at regular cost

So, cost of 4 lanes rented = $4\times 9.75= \$ 39$

Now, out of 10 people who rented shoes, 4 are members. So, the number of non-members is given as:

Non members who rented shoes = 10 - 4 = 6

So, 4 members and 6 nonmembers rented shoes.

So, cost of 6 non members renting shoes = $6\times 3.95=\$ 23.70$

Cost of 4 members renting shoes = $4\times 2.95=\$ 11.80$

Total cost for the party is the sum of all the costs. This gives,

= 39 + 11.80 + 23.70

= 50.80 + 23.70

= $74.50

Therefore, the total cost for the party is $74.50.

5 0

3 years ago