5. Given a function f : A → B. Define the relation ƒ from P(A) to P(B) by f = {(X,Y) C P(A) × P(B) | Y = f(X)}. a. Show that f is a function from P(A) to P(B). b. Show that if ƒ is one-to-one, then f is one-to-one.

Q: Draw the graph of the function f :R → R defined by f (x) = x3, x∈R.

A: We will make a table for f(x)=x3 x -1 0 1 y -1 0 1

Q: 1. Given a function f : A → B. Define the relation f from P(A) to P(B) by f= {(X,Y) Ɛ P(A) × P(B)|Y…

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Q: 3. Is the relation xy = 36 a function? Explain why or why not? Draw this relation.

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Q: A. Plot the following function with clearly labelled axis. x(t) = [1, -2<tsxl, and [0, otherwise]

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Q: Let f be the function from {a, b, c, d, e} to {1,2,3,4} with ƒ(a) = 3, ƒ (b) = 1, f(c) = 2, f(d) = 4…

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Q: 3. Consider the relation f (x) = 2x² – 4. Find the f(x). Be sure to use proper notation.

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Q: Find and provide a sketch of the domain of the function 2 y2 f(r, y) = 9. 4.

A: Given,  f( x,y)=1−x29−y24 To Find: Domain and sketch of the given function.

Q: Let f be a function defined as follows: f(x) = 2.3-2 if x 3. if x > 3. x-3 What type of…

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Q: [9] Let A = {a, b, c, d} and B = {1, 2, 3}. Define a function F: A → B as follows: F3(а, 3), (b, 3),…

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Q: Draw the function of y = x 2 / 3 + x2

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Q: g(t)= fo re² 35 a) 2 e ³s S b) Ze c) e -35 d) c = ³5 -مج -35 53 35 if (/? 3. not in 2 3 5² 2 5³ + ->…

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Q: The figure defines a function f from A={r, s, t, u} into B={a, b, c, d} in the obvious way. Which of…

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Q: Assume that the relation x = √500+ 5y² defines y implicitly as a function of x. Determine y" as a…

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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: 2. Count the number of different one-to-one functions f : {0, 1}' → {0, 1}'. Justify your answer.

A: The solution are next step is

Q: C. State whether or not the following relations are functions. Also, give their domain and range. 1)…

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Q: Let f be the function from {a, b, c, d, e} to {1,2,3,4} with ƒ(a) = 3, f(b) = 1, ƒ (c) = 2, ƒ (d) =…

A: Here given that fis the function from a, b, c, d, e to 1, 2, 3, 4 with f(a)=3, f(b)=1, f(c)=2,…

Q: Which of the following relations is not a function? O a. y = X O b. y= 5 O C. x= y² O d. y = 2

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