The functions h and m are defined on the set R of real numbers by h:x→ ax +b and m:x → cx -d, where a, b, c and d are constants. If h o m = m o h, show that (c-1) b = (a-1) d

Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

A: We know that, Total profit = Total revenue - Total cost

Q: 4. Prove i × (i × Ã) +j× (j × Ã) +kx (k × Ã) = –2Ã.

A: Our Aim is to prove that:-i⏞×(i⏞×A→)+j⏞×(j⏞×A→)+k⏞×(k⏞×A→)=-2A→-(i)

Q: Let A = B = C= {x|x is a real number). Let f : A → B and g : B → C be defined as follows: f(a) = 6a…

A:

Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

A:

Q: a. Let X = {2, 4, 6} and Y = {a, b, c, d'}. Define g : X→ Y by the following arrow diagram. X 2 4 bo…

A:

Q: Refer to the following functions: p(x)=x²+2x-15 q(x)= x+1 x-3 r(x)=√7-x Which of the following…

A: Consider the given functions, px=x2+2x-15qx=x+1x-3rx=7-x i. The composite function is given as…

Q: Let B = a = The function p(t) = 2 + 4(t − 5) + 7(t − 5)², can also be written as p(t) = a + b(t − 2)…

A:

Q: Find real numbers x, y and z such that (x + 4)i + (y – 5)j + (z – 1)k = 0

A: To Determine :-  The real numbers x , y and z  such that   x + 4  i +  y -5  j +  z - 1  k =0

Q: Find all non-negative integer pairs of (x, y) such that (xy-7)² = x² + y²

A: Find all non-negative integer pairs of (x, y) such that .

Q: 1. Let Q(v2) = {a+b/2| a, b E Q}. Prove that Q(/2) = Q[x]/(x² – 2).

A: We have to show that isomorphism means there is function ϕ such that we have to show that it is an…

Q: 9. Write each quadratic relation in standard form, then find the zeros. a) y = 2(x + 1)² - 50 b)…

A: Given :(a) y=2x+12-50(b)  y=-3x-12+48

Q: We know that 1 is a zero of the function f(x) = x3 + x2 - 5x+3 the multiplicity of f at 1 is: Select…

A: We are given that 1 is a zero of f(x)=x3+x2-5x+3 ⇒(x-1) is a factor of f(x)=x3+x2-5x+3 Now, By long…

Q: Let B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3) Show that the function g is surjective.…

A: We are given that B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3). We need to show that g is…

Q: Determine whether the following set of polynomials is linearly independent (1 – t)?, t – 2t2 + t³,…

A:

Q: 5d rd-2a 2b a D. 5e-h If det d Lg h i 1, compute det e If - 2c %3D C 5f-

A: To compute determinant of the given matrix.

Q: (a) Show that if a > 0, then 1/a> 0 and 1/(1/a) = a. (b) Show that if a <b, then a < (a+b) < b.

A:

Q: Let X = the integers. Let Y = {0, 1, 2, 3, 4, 5}. %3D Let f : X Y be defined as the remainder when x…

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Q: Let f: AB and 9: B→C be defined as follows: f(a) = 4a² +2 and g(b) = 26-7 Compute the following: (a)…

A: Let A=B=C=x|x is a real number Let f:A→B and g:B→C be defined as  fa=4a2+2andgb=2b-7 Hence…

Q: Part J only

A: Note: Since the student has mentioned to solve only part (j), so we are solving accordingly to part…

Q: domain f(x) = V 26 – x Vx – 6 + V 20 – x -

A: See the attachment

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: b) Find 4°f(x) if f(x) = (3x+1)(3x+4)(3x+7) ... (3x + 19) %3D

A: We will answer the first question only as we don't answer multiple question at a time. Please…

Q: example of two functions t₁ (n) and t₂(n) that satisfy the relations t₁(n) w(n²), t₂(n) = w(n²) and…

A: Given that the two functions t1(n) and t2(n) that satisfy the relations                t1(n)=ω(n2),…

Q: In Exercise, verify that S and T are inverses.

A: Given, S and T are inverses if S∘T=T∘S=I

Q: Consider z1 = 1 - j2 and z2 = -2 + j3. Determine Im (21)?

A:

Q: (a) Let x1,.., Xn+2 € R". Show that there must exist some sets A and B such tha i. ANB=Ø, ii. AUB=…

A: Let x1,x2,....,xn+1∈ℝn We take n=5. then x1,x2,x3,x4,x5,x6,x7∈ℝn There exists two sets A and B,…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.