Example 1.5. Let X = R? x R² and d1 : X R, such that, (1) di(x, y) = d;((r1, 12), (Y1, Y2)) =| ¤1 – Yı |+ | #2 – 42 | (2) d2(x, y) = d2((x1, T2), (Y1; 42)) = Max{| x1 – Y1 |;| #2 – 2 |} Then (X, d1) and (X, d2) are metric spaces. Proof. Exercise.

Q: If f(x, y) = 1 then 3(3x–2y) * is given by: | O None of these 4 (3x-2y)3 (3x-2y)3 - (3x–2y)³ 4 -…

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Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

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Q: Let f(x) = Vr - 5, g(x) = , h(a) = , Find go((gof)+h(x)) at x=-1? 2-9'

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Q: 7. Which is the domain of the function x + 8 + V3 – x – - 2 5, f (x) = Vx +7+ Vx + 3 ? (-0, 3) – {2}…

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Q: 25. If f(x) = 3x² – x + 2, find f(2), f(-2), f(a), f(-a),

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Q: 3.) flx) x+2

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Q: If f(x, y) = %3D

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Q: The zeros for Ax) = x-4x-9x + 36x are 1) (0,+3,4) 2) (0,3,4) 3) (0,±3,-4) 4) (0,3,-4)

A: Using method of synthetic division to find factors of f(x).

Q: If fx) x) f(1) = and f(1) -2, find 1) -16/13

A: Formula used:

Q: Find x(t) for the following: X(s) = (a+1)(2+2) (-1)(s-2) Select one: O a. ¤(t) = (-6e t + 12e-2#…

A: Given:   X(s)=s+1s+2s-1s-2    Take partial fraction of s+1s+2(s-1)(s-2)…

Q: 3.2 X(x²-1)-y=xy* ;y(2)=-

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Q: a) If y = 3x – 2, x = 3t + 2, and t = 3k – 2, find b) Express y as a function of k ify = 2x + 5, x…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: e equation of

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Q: Example 9. Classify each relation as constant, linear, quadratic, or neither. a) y = x² + 5x + 6 b)…

A: The solution is given below:

Q: 16. (T/F) If A and B are 3 x 3 and B = [b₁ b2 b3], then AB [Ab₁ + Ab₂ + Ab3]. =

A: Given: A and B are  3×3 and let AB=Ab1+Ab2+Ab. To Find: Whether the following statement is true or…

Q: 20) For the the function f(x) 5x-2, find f(4a+ 1) A) a-1 C) 9a-3 B) 20a - 1 E) 20a + 3 D) 9a – 1

A: Given that  f(x)=5x-2 Find f(4a+1)

Q: 4. Let f-(x) = g(x) = x-5, k-1(10) + 7 = 10 and h(x) = then find: b. Domain of h(x). c. (hof)(2). (Z…

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Q: I. If f(x, y) = x² – y² + 4xy – 7x + 10, find (a) f(2, 1) (c) f(x + h, y) (b) f(-3, 5) (d) f(x, y +…

A: topic - functions note : As per bartleby guidelines, we are supposed to answer only first three…

Q: Which of these functions has a y-intercept of (0,9) ○ A) ƒ(x) = 9x² + 4x + 2 B) f(x) = 9(x-3) (x +…

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Q: 4. For f(x) = x² – 3x, evaluate a) f(2) [2,3,3] c) the value of x when f(x) = 4 b) f(m + 1)

A: Given,              f(x)=x2-3x

Q: If f(x) = x + 9 – x and g(u) = u + V9 – u, is it true that f= g? Yes No

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Q: If f(x) = x*(3x + 2)°, find f(x). O x(3x + 2)7(11x + 8) O x³(3x + 2)7(36x + 8) O x³(3x + 2)7(20x +…

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Q: 3(x-5) = 1 %3D 27 3. 3. 3D 3 = 3 X =

A: An exponential function is a one-to-one function. So if we have ax=ay then we have x=y. Solving an…

Q: What is the y-intercept for f(x) =;|2x + 6| – 1? А. (2,0) В. (о,-2) C. (0,6) D. (0,-1) E. not given

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Q: 2t – 5, t 2

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Q: The range of the function f(x, y) = 6 - 4 - x2 - y² is (-00, 6] o [4, 0) [4, 6] (-0,4] [6, 00)

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Q: 1. Let f(x) = 3x + 1, g(x) = 7 – 2x, and h(x) = x² – 4.x + 5. Find the following: a) (f + g)(2) b)…

A: 1. Given, f(x)=3x+1g(x)=7-2xh(x)=x2-4x+5

Q: 6. The domain of y = v1 – x? is

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Q: 12. Let f(z) =,h z 0. Then f(2 + h) – S(2) h A) – 4+ 2h 1 B)- 4+ 2h C)-- 4- 2h 4-2h

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Q: If 6x³ +x* –y³ 2x² +y² f(x, y)= if (x, y) (0, 0) if (x, y)= (0, 0) then f,(0, 0)= O does not exist

A: Thanks for the question :)And your upvote will be really appreciable ;) Correct option (A) does not…

Q: Let f(x) = Vx and g(x) = x³ +1. Find 29 a) f(g(2)) b) g(f(4)) c) f(F(16)) d) g(g(0)) e) f(2+ h) f)…

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Q: 4 y-fx) 36) Use the graph of the quadratic function to write it as: f(x)-a(x -h)'+k 26 -4-2

A: The graph is downwards parabola whose equation is (y-k)=a(x-h)^2, where (h,k) is the vertex of…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.