Question

Prove the Given theorem: 

Let f : X → Y and g : Y → Z be two invertible functions. Then gof is also
invertible with (gof)-1 = f-1og-1



Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Algebra

Other

Related Algebra Q&A

Find answers to questions asked by students like you.

Q: A rectangular garden has an area of 14 m2 and a perimeter of 18 meters. Find the dimensions of the r...

A: A rectangular garden has an area of 14 m2 and a perimeter of 18 meters. Find the dimensions of the r...

Q: A store in Minnesota advertises that on a holiday, everything is 20% off. A person buys shoes for $4...

A: The total price before discount is =  $(40+10)= $50.

Q: Solve simultaneously for x and y2 + y= -2x-2x2+ 8xy + 42= y

A: Click to see the answer

Q: Vera and Vikki are sisters. Vera is 4 years old and Vikki is 13 years old. What age will each sister...

A: Given that Vera is 4 years old and Vikki is 13 years old. Obtain the age of each sister when Vikki i...

Q: A wool tapestry is 32 years older than a linen tapestry. Twenty years ago, thewool tapestry was twic...

A: Given: A wool tapestry is 32 years older than a linen tapestry. Twenty years ago, thewool tapestry w...

Q: Show that the function f : N→ N, given by f (1) = f(2) = 1 and f(x) = x – 1,for every x > 2, is o...

A: Given, the function f : N→ N, given by f (1) = f(2) = 1 and f(x) = x – 1, for every x > 2.

Q: {x|x is an even whole number less than 6}

A: To find:x such that x is an even whole number less than 6.

Q: Ikentie each esxpression a lolynomal, for each pognomia, quue te Legre and idennA aus each eupressiO...

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: At a recent motorcycle rally, the number of men exceeded the number of women by 216. If x represent ...

A: Given, the number of men exceeded the number of women by 216 and x represent the number of women.

Q: The doctor tells Laura she needs to exercise enough to burn 500 calories each day. She prefers to ei...

A: Let the number of minutes Laura runs be x.And the number of minutes Laura bikes be  y.

Q: How much of a 70% orange juice drink must be mixed with 44 gallons of a 20% orange juice drink to ob...

A: Let x gallons of 70% orange juice drink must be mixed with 44 gallons of a 20% orange juice drink to...

Q: If A and B are symmetric matrices of the same order, then show that ABis symmetric if and only if A ...

A: Given that, A and B are symmetric matrices.

Q: How do I write x2 + y2 + 8y + 2 = 0 in standard form.

A: Given,

Q: Explain zero matrix along with an example.

A: Zero matrix is a matrix in which all elements are 0’s.

Q: Use front-end rounding to find an estimate of the answer. Then find the exact difference. 312.329 -8...

A: Estimation the difference.

Q: Two cubes have side lengths that are equal to 2x and 4x. How many times greater than the surface of ...

A: Surface area of cube of side length "a" is given by 6a^2. 

Q: State the Properties of matrix addition.

A: Addition of MatricesTwo matrices may be added only if they have the same dimension. That is, they mu...

Q: x2-5x-36=0

A: To determine the solution of the quadratic equation.

Q: The FAA now figures the average checked bag to weigh 28 pounds. This is up from a previous figure of...

A: Given:

Q: How many times does 641 go into 2^2^5

A: We are going to calculate that how many times does 641 goes into 2^2^5.

Q: Let β ={x1,...,xn} be a subset of Fn containing n distinct vectors, and let B denote the element of ...

A: Assume that β ={x1,...,xn}  is a basis for Fn.Let B denote the element of Mnxn (F) whose jth column ...

Q: Ryan remembers numbers using images that look somewhat like each number: 0 is a ball, 1 is a stick, ...

A: Given that  0 is a ball, 1 is a stick, 2 is a hanger, 3 is a comb, 4 is a kite

Q: What is mLSQR? P. S. 2x 3х m ZPQR = 80° %3D MZSQR equation: %3D

A: Given that angle PQR = 80 degree.

Q: Solve the equation : 5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13

A: The given equation is,

Q: Jules goes on a hike that will last 5 hours total. She brings 12 cups of water. After an hour, she h...

A: According to the given information:Number of cups of water Jules bring on hike = 12After an hour she...

Q: Hey can I get the bottom part answers D-k

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3 (d,e,f). Please resubmit the questi...

Q: Find the value of y:  logy32=5

A: Given, expression

Q: Passing through (-3,7) and perpendicular to the line with equation 2x+3y=7The answer is provided in ...

A: Given equation of line

Q: Lucy took three tests. If her median score was 88, her mean score was 87, and the range was 11, what...

A: Given:Median = 88Mean = 87Range = 11

Q: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describi...

A: To determine the integer equation describing the pay check.

Q: You invested $10,000 in two accounts paying 5% and 8% annual interest, respectively. If the total in...

A: Click to see the answer

Q: Jenn can rent a moving truck for either $99 with unlimited mileage or $49 plus 80¢ per mile. For wha...

A: Let x be the number of miles.

Q: What is mZABC? 2y°/y° LABC and LCBD are supplementary. MLABC = equation:

A: Given that the angles ABC and CBD are supplementary. It is known that the sum of the supplementary a...

Q: I need help with answering this question please.

A: At a recent motorcycle rally, the number of men exceeded the number of women by 216. If x represents...

Q: Given that log 2 = x, log 3 = y and        log 7= z, express the following expression in terms of x,...

A: We will write 0.3 as fraction. That is 3/10

Q: In April 2011, Consolidated Edison (ED) stock cost $50 per share and yielded 5% per year in dividend...

A: Let there are x ED shares and y NGG shares.ED share and NGG share both  costs $50 eachYou have inves...

Q: A company found that -2p + 1000 models the number of TVs sold per month where p can be set as low as...

A: Given

Q: Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the po...

A: It is given that, the distance of point P from the origin is same as that of distance of point Q fro...

Q: ObquuTC. 37. The hypotenuse of a right triangle is 7 feet long. One leg is 4 feet shorter than the o...

A: Let  the length of legs of right angled triangle be x and x-4 ( in feet ) . Hypotenuse of the triang...

Q: Richard Penta recently restored a 1965 mustang coupe. He will park it in a new parking area in his b...

A: Given information, dimensions of rectangular parking area are 22/3 yards and 13/3 yards.The cost of ...

Q: Convert 2 3/4 to a decimal number.   0.75   1.50   2.3   2...

A: The given mixed number is