Start your trial now! First week only $4.99!*arrow_forward*

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^{-1}og^{-1 }

Tagged in

Math

Algebra

Find answers to questions asked by students like you.

Q: Suppose that <*,*>1 and <*,*>2 are two inner products on a vector space V. Prove that &l...

A: Click to see the answer

Q: When solving systems of equations we have at least two unknowns. A common example of a system of equ...

A: Let he has x quarters and y dimes He has total 60 coinsSo, x+y=60

Q: Find two consecutive integers whose product is 210.

A: Find two consecutive integers whose product is 210.

Q: Solve for the indicated variable. P= a+b+c for c.

A: Given that P= a+b+cWe have to solve for c. That means we need c alone on a side

Q: Let A be the set of all students of a boys school. Show that the relation Rin A given by R = {(a, b)...

A: It is given that, A is the set of all students of a boys school.Show that R is an empty relation.Her...

Q: Explain Equality of matrices. Give a suitable example.

A: Equality of matrices:Two matrices are equal if all three conditions given below are satisfied: · Bot...

Q: What is meant by algebraic expression? Explain giving example

A: Algebraic expression:

Q: Divide me by 7, the remainder is 5. Divide me by 3, the remainder is 1 and my quotient is 2 less tha...

A: Given:Divide me by 7, the remainder is 5. Divide me by 3, the remainder is 1 and my quotient is 2 le...

Q: Solve for 'x' : 9.2x-1= 2.3x

A: Click to see the answer

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