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
Savatey [412]
3 years ago
11

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

sing interval notation.

Mathematics
1 answer:
Kryger [21]3 years ago
8 0

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)



You might be interested in
1. Rudy paid for 5 trees to be delivered.
sertanlavr [38]
Here you go, hope it helps!

8 0
2 years ago
Describe how to determine if a number is a solution to an equation.
marin [14]

Step-by-step explanation:

Determine whether a number is a solution to an equation.

Substitute the number for the variable in the equation.

Simplify the expressions on both sides of the equation.

Determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.

Hoped that helped:P

5 0
2 years ago
Read 2 more answers
Find the measure of angle M.
frutty [35]

Answer:

About 72 degrees

Step-by-step explanation:

3 0
3 years ago
Identify the correct equation for the linear function.
Natasha2012 [34]
D) 12x+9
the slope is 12 and the intercept is 9
7 0
3 years ago
Determine if the following table represents a linear function. If so, what’s the rate of change?
VLD [36.1K]
Yes at the rate of change is 3/2
3 0
2 years ago
Read 2 more answers
Other questions:
  • What is the solution to the system of equations? Use the substitution method. {y=−2x+5 3x−4y=2
    12·2 answers
  • 1-s=6-6s help meeeeeee
    6·1 answer
  • Karin wants to use the distributive property to find the value of 19·42+19·58 mentally. Which expression can she use?
    10·1 answer
  • Hi! I really need help with this question and please help me if u can. I'll mark you as BRAINLIEST.
    6·1 answer
  • Ruiz needs to buy a countertop for a kitchen. He calculated the area to be 16 square feet. The actual area is 15.4 square feet.
    5·2 answers
  • Explain the difference in meaning between 1-3 and -3 help help :0
    7·1 answer
  • At the start of the week, Ladasha’s checking account had a balance of $34. She deposited $50 each day for three days. She made a
    14·2 answers
  • Amir invest 4,000 in a 5 year cd paying 3.5% interest. How much interest will he make on the cd in 5 years? The simple interest
    5·1 answer
  • In the diagram, N, O, and P are congruent. Find x.
    9·1 answer
  • Amanda runs 10 miles in 56 minutes. how many miles does she run per minute
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!