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Kisachek [45]
2 years ago
9

HELP ME PLEASE!!

Mathematics
1 answer:
Vedmedyk [2.9K]2 years ago
6 0

Did you ever find the answer because i need it !

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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
3 years ago
Select the correct answer.
Alla [95]

Answer:

Step-by-step explanation:

7 0
2 years ago
Tehara has read 115 pages of a 305 page book she reads 10 pages each day how many days will it take to finish
scZoUnD [109]

Answer: 19 days

Step-by-step explanation:

305-115=190

190 divided by 10= 19

7 0
2 years ago
Read 2 more answers
A bird was sitting 16 feet from the base of an oak tree and flew 20 feet to reach the top of the tree. How tall is the tree?
Eddi Din [679]

Given:

A bird was sitting 16 feet from the base of an oak tree and flew 20 feet to reach the top of the tree.

To find:

The length of the tree.

Solution:

A bird was sitting 16 feet from the base of an oak tree.

Vertical distance between bird and base = 16 feet

Then the bird flew 20 feet to reach the top of the tree.

Now, the vertical distance between bird and base = (16+20) feet

So, length of the oak tree is it the sum of 16 feet and 20 feet.

\text{Length of the oak tree}=16+20 feet

\text{Length of the oak tree}=36 feet

Therefore, the length of the oak tree is 36 feet.

5 0
2 years ago
Emma works in a department store selling
IceJOKER [234]

Answer:

$320

Step-by-step explanation:

She made $800 of sales right and her paid commision is 15% so there she receives:15%×$800=$120+a guaranteed $200 dollars each week =$320

7 0
2 years ago
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