Exercise 5 Determine a value of 8>0, that satisfies statement: If 0 < x - 3|<8, then f (x) +1|<1. YA 5+ -5 -4 -3 -2 -1 15 4+ 3+ 2+ 1+ 0 -1+ -2+ -3+ -4+ -5- 1 2 3 Limits 4 5 X

Q: b) Let c be any constant. Show that the function f(x) = x° +x +c_cannot have two zeros. (Use the…

A: Given that function f(x)=x3+x+c where c be any constant. For finding the real root of function we…

Q: (d) What are the domain and range of the function y = 2ƒ(x)? (Use symbolic notation and fractions…

A: The function  has a domain  and a range .The aim is to find the domain and range of

Q: Let f (x) = x2 - 3 and g(x) = 2x + 1. Find (fg)(2). 2) ***HINT: Start by first finding f (2) and…

A: The given functions are,

Q: Let f(x) = x² - 6x and g(x) = 4 - x². ▪ (f+g)(4) = (f-g) (4) = (fg)(4) = (4) (4)

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Q: х2 — 2х-15 x2 — х— 20

A: We have to evaluate the following limit: limit as x tends to 5, [(x2 - 2x - 15)/(x2 - x - 20)]

Q: -4 f(x) = {x – 2 (-2x + 4 if x< - 2 if - 2<x< 2 if x22 © 2005, Agnes Azzolino Permission is grantad…

A: Given function is piecewise function

Q: State the theorem for Limits Preserve Inequalities.

A: We have to state the theorem for limits preserve inequalities .

Q: Evaluate limr→∞ -8x³+10x 7x-x2 2 8.

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Q: (c) What are the domain and range of the function y = f(2x)? (Use symbolic notation and fractions…

A: The function  has a domain  and a range .The aim is to find the domain and range of

Q: 11x + 3 lim 9x2 4x + 5

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Q: - For the functions f(x) = x + 2 and g(x) = x - 3, which expression has the greatest value? a)…

A: We have given:Find the composite function :Find the composite function :

Q: x -4 ifx<2 Determine f(2) if f(x)= {2-x if 2 <x<4. x-2 if 4 <x

A: Given,           fx=x2-4if x≤22-xif 2&lt;x≤4x-2if 4&lt;xTo find : Determine f'+2.

Q: 2y dr - y dy y (x-2y) dy, y(0) =-1 O x = 2y - e +3 %3D a y = 2r- e+3 0x= 2y-e+3 O x = 3y + 2e +1

A: Given DE is 2y dx-y dy=y(x-2y)dy ⇒dx-12dy=12(x-2y)dy⇒dx=121+x-2ydy⇒dxdy=12+x2-y⇒dxdy+x-12=12-y Which…

Q: 12. Rewrite the following as piecewise-defined functions: (a) f(x) = 5|2x - 3| (b) h(x) (c) g(x) = X…

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Q: What is the domain in interval notation of the function scrt(x-4)/scrt(x-6)

A: Solution:function :- x-4x-6∵we know that the value in the square root can not be…

Q: 7. If f(x) = 3x + 5 and g(x) = x + 2x - 3, determine x such that f(g(x)) = g(f(x))

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Q: 10. Use the function k(x) = x + 4x + 3. a) Write explicit equation for three functions f(x), g(x),…

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Q: Determine the interval(s) where the function ƒ(x) = −(x − 5)² is increasing. Submit your answer in…

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Q: (f) Evaluate f(-1) and f(1). Can you conclude that there is no zero on the interval (-1, 1)? Explain…

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Q: Let fx)=√√-Fit (a) the set of real values of x for which fis real and finite; (b) the range of f.…

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Q: If fixgy is continuons and x is connected, then so is f(x). 50

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Q: x-3/x+1 &gt; 0

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Q: 2. Find the domain and range of f(x) = Express your answer using set notation. x+7

A: GIVEN: f(x) = 2x + 7

Q: The piecewise function f is defined below.  ?(?) = }       3? − 1   if  ? ≤ −2…

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Q: Evaluate the limit 7x3 – 2x2 – 2x lim 2 — 4х — За3 x → 00

A: limx→∞7x3-2x2-2x2-4x-3x3 ⇒ limx→∞7-21x-21x221x3-41x2-3 (divide numerator and denominator by x3)

Q: Evalvate f(f(f(2) X+5 for x5

A: