Let f: X→ Y and g: Y → V be functions. Show the following: (a) f is injective ↔h : Y→ X such that ho f = idr (b) f is surjective 3h: Y→ X such that foh = idy Use: ←

Q: Let f(x, y) = 125-3x²-2y2² Evaluate f(0, 3)

A: f(x,y)=sqrt(125-3x2-2y2)Find f(0,3)

Q: Let f(x)=xsinx+V1-x Evaluate f'(-). Select one: а. 2 b. 0 C. d. 3

A: According to product rule of differentiation and according to power rule of differentiation .

Q: C) Write a function f(x, y) such that the domain of f(x,y) is D = {(z,y) | 2² 29-y²). Also provide a…

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Q: Let f(x) = m1x + a and g(x) = m2x + b, where m1, m2, a, and b are constants. Determine the necessary…

A: f∘g=g∘ffgx=gfxfm2x+b=gm1x+am1m2x+b+a=m2m1x+a+bm1m2x+m1b+a=m1m2x+m2a+bm1b-b=m2a-abm1-1=am2-1

Q: f:R - R S6 – x2 x 2 1 x < 1 fx 4x + 1 x=1, x= -1-

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Q: Given the function fA(x) = x², g(x) = 3x – 4, find the composite function gof (where gof'means…

A: I have find inverse of f the composition

Q: 5. (a) Let f: S T be a function, and A CT and BCT be subsets. Show that (A-B) = f-1(A) - f-(B). ww

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Q: Let f(x) = v9x+ 8 and g(x) = x+9 be functions from R to R. Find the following. a) (f • g)(x) = %3D…

A: We are given f(x)=9x+8 and g(x)=x+9 and we need to find different composition of the function.

Q: of and ду of For the function f(x,y) = In (x+ 3y), find

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Q: 3. Find the domain of the following functions: a.) f(x) = V1-x Inx b.) f(x) = Vx - 1lr

A: solutionsince the given (3)(c)f(x)=1-xlnx(b) f(x)=x-l ln(x)use have to find the domain of the…

Q: Q7. Check if the following functions are Orthogonal or not? fi(x) = x°, f2(x) = x² + 1 [-1, 1] on…

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Q: Consider the function of two variables defined by: f(x,y) = (x3y4) / (x-7210)2+(y-9245)2 What…

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Q: Find x-intercepts of the function: x2 – 9 f (x) = Зх + 1 Select one: O a.x = 3 O b.x= -3, x= 3 C. X=…

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Q: The domain of the function За + 5у is 2? + у? — 4 f(x, y) - >

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Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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Q: Determine if F = x²yî + (xyz +29)ĵ – x²y²k is conservative or not %3D

A: For vector field F⇀=ui^+vj^+wk^ Curl(F)=i^j^k^∂∂x∂∂y∂∂zuvw   For vector field F⇀ to be conservative…

Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

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Q: If f(x) = Vx +1 , g(x) = Vx – 1, find the domain of f +g. %3D

A: Domain is set where function is defined

Q: For the function, evaluate the following. f(x, у) %3D 0.7x + 0.4у — 0.04ху (а) f(0, 0) (b) f(1, 0)…

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Q: Let f(x, y) = √√/175 – 3x² – 4y² Evaluate f(1,4)

A: Given :To Find :

Q: The absolute Extrema of the function f(T) = -x-* -21/3 +r on the interval [ 8, 1] are Select one: a.…

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Q: Is the cobb-douglas function strictly concave when a1 +a2 <1 when

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Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

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Q: Determine whether the function f : R\{2} –>R\{0}, defined by f(x)=(1/(x-2)) is bijective or not.

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Q: Determine the domain and range of the function f: {r,s,t,u} ➔ {A,B,C,D,E} defined by f(r) = A, f(s)…

A: Domain of a function is the set of possible values of independent variable. The domain of given…

Q: Let f(x) = ∥x∥. Find out its conjugate function f ⋆ and prove your conclusion.

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Q: An environmental engineer wants to evaluate three different methods for disposing of nonhazardous…

A: GIVEN

Q: Q1. Let f: N x N R be defined by (a + 1)(a + 2b) f(a, b) – 2 Show that the image of f is contained…

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Q: f(u) = u + 1 h(u) : Vu + 1 p(u) = 1 - 4u2 q(u) = (1 – 4u2)9 g(u) = Vu + 1(1 – 4u2)9

A: Given functions are,