Let f C D be a function, with C being the domain and D being the codomain. Show that for any C₁, C₂ C C f(C₁ C₂) ≤ f(C₁) nf(C₂)

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A: we need to find the inverse of the function.

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: Determine whether the given set of functions is linearly independent on the interval (-o, ∞). f1(x)…

A: The solution is given as

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Q: determine the continuity of the function at a.

A: The objective of this question is to determine whether the function f(x) = 1/(x + 2) is continuous…

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: Determine and graph the domain set of the function f(x, y) = ln(x²+9y2-81) ==

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Q: Prove that the linear function f(x) = ax+b is continuous.

A: To prove that the given linear function is continuous.

Q: 3. Let f : A → B. Then 18f = f and f1a = f. Hint. You may use the fact that fg, for functions f, g,…

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A: Given :To Find :

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Q: Determine whether the following function is continuous at the given point z- 3z+ 14z -5 f(2) 3z -1…

A: A function fx is continuous at x=a if limx→a-f(x) = limx→a+f(x) = f(a)  Given: fx=3x2+14x-53x-1…

Q: Use the definition to prove that the function in f(x) = 2x-3 is uniformly continous.

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Q: Consider the table of values for the function f(x). X 1 2 W|N 3 4 a) 3 b) 4 O c) 1 y = f(x) 3 1 What…

A: Given query is to find individual function.

Q: Find fay (1.2) for f (x, y) = x²In(7 + y) +. 35 19 36 36 19 35 36 36

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Q: Show that the function Arg(z) is not continuous on each point of the non-positive real axis.

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Q: (c) Evaluate the Riemann integral ₁¹(x) dx by using definition with the parti- tion 2n=1,2}, n+1 =…

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Q: Determine where the function f(x) = O A. (-∞, ∞) 1-00 O B. O C. O D. 3 3 3 (-∞0,²21) U ( 212,00) N/W…

A: we have to find out the values of x where function is continuous.

Q: 2. Let m and b be rea If fis both continuo

A: Topic:- calculus

Q: For Exercise, a function is given a. Find f(x + h). b. Find I* + h) – f(x) f(x) = x2 + 4x

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Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

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Q: let F be the function from R to R defined by: f(x) =x². Find f–¹({1})

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Q: Suppose further that a <c< b. Which of the following is a property of an integral? O Option 1 Option…

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Q: Let f(x) = x³ – 6, – 3 < x < - 1 The domain of f- is the interval [A, B 1 where A and B = %3D

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Q: Evaluate the Riemann integral f'(x) dx by using definition with the tion = {₁,"+11/ n Pn= i=1 n+1…

A: Given Data: Let the function f:R→R be defined by fx=-1x2x≠0,0x=0To evaluate the Riemann integral…