Let g : R → R be the function g(t) = t, and let B = [-3, 1] U [2, 3]. Express the set g(B) as an interval, and provide a proof for your answer.

Q: Let f : R → R be a function with the following property: |f (a) – f(b)| < 4|a – b| for all a, b E R.

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Q: f= (2xy+ 3x²)ē+ (x² – 2yz + 2y)ē, – (e² + y²)ēz

A: Given

Q: 3. Let f(x) = x² + 3 and g(x) = Vx – 3 be functions defined on [0, ∞) and [3, 00), respectively. i.…

A: According to question,  Given functions, f(x) = x2+3, g(x) = x-3 Function fx defined on interval :…

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: Consider a function f whose domain is the interval [a, b]. Show that if |f(x) − f(y)| ≤ (x − y)²,…

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Q: let f be the function x²-C for x< 5 flx)=3x+5c for X Z 5

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Q: Let f : R → R be a function defined by f(x) = Decide whether it is an injection, a surjection, 1+ x2…

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Q: Consider f = {(x, y) : x ∈ N and x + y = 5}. Write out some elements of f. What are the domain and…

A: Given: f={(x,y): x∈N and x+y=5} The domain of a function f(x) is the set of all values for which the…

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: - Consider the function f(x) = 2x² - 16x 5 on the interval [2, 6]. Find the value(s) for c that…

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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: lim 3i 4 +

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Q: XI. Refer to the functions f, g, and h defined here. f(x) = 1/x, g(x) = 2 vx, and h(x) = x2 -1…

A: Using rules of functions.

Q: Use a formula to express w as a function of t if w - V4s + 5 and s- ef - 1.

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Q: Let X = { n Î Z | 1 £ n £6 } and consider the two functions f : X ® X , g : X ® X , expressed in…

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Q: Let V be a vector space and x, y, z E V. Suppose that any v E V can be written as a linear…

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Q: Consider the set N²= NX N, the set of all ordered pairs (a, b) where a and b are natural numbers.…

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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: f(x,y)=x² + 3y + 7. R is he region shown in Fig. 5 (include the boundary). y =2-x y-4- R Fig. 5

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Q: Let f : R → R be defined as                   f(x) = 10x + 7. Find the function            g : R → R…

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Q: Show that the function f : R → R given by f(x) = x3 is injective.

A: To show the given function is injective(one-one), first calculate the value of function at two…

Q: f'(t) = tf(t). HINT: Write f'(t) – tf(t) = 0 and multiply the equation by e-2/12.

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Q: Find c such that the function 1² – 7 I c is continuous everywhere. C =

A: Given query is to find the value of c.

Q: f (x,y)= y² -2x² +10. Ris the region bounded by the parabola y = x and the line y = 4.

A: According to the given information, it is required to find the maximum and minimum value of f on the…

Q: Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined byf(x) = ax + b, for some…

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Q: what sets X and Y is the function X Y defined by 3x f (x) = x +4 %3D ijection?

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