23-24 How would you "remove the discontinuity" of f? In other words, how would you define f(2) in order to make f continuous at 2? x? - x - 2 23. f(x)

Q: х- 3, x2

A: Given:      Let fx=x-34-x2x2-3x<-2-2≤x≤2x>2              gx=x2-x+1   For x=-12        fx=x-3 ,…

Q: 5а — 2 if x 10 If f(x) is a function which is continuous everywhere, then we must have b :

A:

Q: (a) What are the x-values for which the function appears to be not continuous? O Function g appears…

A: If function g is connected at all points in the given graph , it is continuous for all values of X.…

Q: 4. (a) Suppose that a function f satisfies |f (x)| < |x| for all x. Show that f is continuous at 0.…

A:

Q: Question 29

A: It is known that, the domain of the function is set of all set of all possible values of x for which…

Q: #26

A: 26. The given function is,

Q: тӕ 11 if x - 4 If f(x) is a function which is continuous everywhere, then we must have = u

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Q: - 7 f(x) (x – 2)(x +1) is continuous. f is continuous on

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Q: 1- 10 Consider the function defined by (x3 -3 f(x) = {? +1 if x 2 Is it continuous at x = 2?…

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Q: 59. The function f is neither left- nor right-continuous at x = 2. 6.

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Q: Example 1: The function has a removable discontinuity at 2. How would you redefine f(2) to make f…

A: Given: also, this function has a removable discontinuity at 2.   To determine: redefine f(2) to…

Q: - Graph the function 1, xS-1 -x, -1 <x <0 f(x) = x = 0 0 <x< 1 xz 1. 1, -X, 1, Then discuss, in…

A: Given  The function is  One side discontinuity : To draw graph

Q: 1 0.5 -5 -4 -3 -2 1 2 f -0.차 -1 -1.5 -2 5. Is the function continuous at x = -3? 6. Is the function…

A: topic - continuity of a function

Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

A:

Q: 5а — 1 if a 7 If f(x) is a function which is continuous everywhere, then we must have b =

A:

Q: (A) True (B) False If f(x) is continuous, f(-1) = 2, and f(2)= -1, then f(x) has a root in [-1,2].

A: This question is related to intermediate value theorem .

Q: тх -11 if x < -4 Let f(x) = + 10x - 7 if x - 4 If f(x) is a function which is continuous everywhere,…

A:

Q: 1. Find the numbers at which f is discontinuous. At which of these numbers is f is continuous from…

A: To check whether the function is continuous or discontinuous calculate the limits as shown Now…

Q: x3- 3 if x 2. B-10. Is the function defined by f (x) { continuous at x 2? Differentiable I at x =…

A: Given piecewise function is: fx=x3-3if x≤2x2+1if x&gt;2 To determine whether function is continuous…

Q: 5. If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

A: For the given question, we can write the function (f÷g)(x) as:f(x)g(x)=tanx3x-32Hence, the domain of…

Q: 2х — 2 Find (f-1)'(a) for f(x) = when a = — Зх — 1 - Enter an exact answer.)

A:

Q: 3 1. Is the function g(x) = if 0 < x < 1, if 1 < x < 4, continuous on [1,4]? on (-0, 0)? 3 – x2

A: As per guideline we have to solve one question

Q: Please show steps and include answer

A: The function is given as,

Q: 3. Determine whether the function is continuous at r = 5. 2²-42-5 2-5 x 5 D

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Q: Classify the type of discontinuity manifested by the function   f(x)=1/(x-1)2

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Q: 6. Does there exist a continuous function on the interval [0, 2] such that f(0) = 0, f(2) = 7, and…

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Q: 8. True or False A function f is decreasing on an open interval / if, for any choice of x, and x, in…

A: A function f(x) is increasing if f(x2) ≤ f(x1) whenever x1 &lt; x2. It is strictly increasing if…

Q: 9. If f (x) = prove that f (xr) is an even function. et -1 2

A: A function f(x) is said to be even if we have f(-x)=f(x)

Q: -x ifx1 function f. Where is f discontinuous? Justify your answer using the definition of…

A: We first make a table for the function x -4 -1 0 0.5 1 2 3 4 y 2 1 1 0.5 DNE 1 4 9 Then we…

Q: Q4) Test the continuity of the function f(x): - 2< x < 0 0< X<1 X = 1 F(x) = Зх —2 2x +1 3

A:

Q: 23-24 How would you “remove the discontinuity" of f ? In other words, how would you define f(2) in…

A:

Q: ample 23: Show that the function f(x)=1-1-x is continuous on the interval [-1. 11.

A: A function y=f(x) is continuous in an interval [a,b] if it exists for every x∈[a,b] In other words a…

Q: - We define the function f: R -> R as follows. Let f(x) = x-2 for X2, and f(x) = a for x=2. What…

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Q: 2. Write TRUE if the statement is correct. Otherwise, FALSE. 5x, xs-1/2 x >-1/2 Let g(x) =1 2x+1 At…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 10 if x < - 8 тх - Let f(x) x2 + 7x – 2 if a 2 - 8 If f(x) is a function which is continuous…

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Q: Only question 21Explain why the function is discontinuous at the given number a. Sketch the graph of…

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Q: 2- 62 Suppose that f is a function given by { |x+ 5| x1/5 if x 32. (a) At which x-values does f not…

A: Topic :- Functions

Q: x + 4 if x 3 Let f(x) = (10 – 2x Is it possible to define f at x = 1 in such a way that f'becomes…

A: if f(x) is continuous at x=1 then  limx→1-f(x)=limx→1+f(x)limx→1-f(x)=-x=-1

Q: 7. Find all constants a, b that make f continuous at x = 2. (Use limits and definition of…

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Q: Q4) Test the continuity of the function f(x): - 2 < x < 0 0< X <1 X = 1 F(x) = 3x - 2 2х + 1 3

A: Fx= 3x-2  -2≤x&lt;02x+1     0≤x&lt;13       x=1 We know that a polynomial function is always…

Q: Find the discontinuities of the function 2х — 1 - if 2 < x x +1 1 Let G be the function defined by…

A: Given,

Q: (b) The function f is defined by 5 X7 5 Determine the values of A and B if f is continuous at x=--…

A: the given function f is defined by: fx=Ax2-6,       x≤-54Bx+A,          -54&lt;x&lt;725,…

Q: 16 if I - 8 If f(x) is a function which is continuous everywhere, then we must have m

A: Given function is f(x)=mx-16  ,x&lt;-8x2+9x-8  ,x≥-8 Firstly, we will find limit of f(x) as x…

Q: 2. Find numbers at which f is discontinuous. At which of these numbers is f continuous from the…

A: Solution

Q: * - 36 Define g(- 6) in a way that extends g(x) = to be continuous at x= - 6. x + 8x + 12 g(- 6) =|

A: topic - limits

Q: (г? + 4х — 21) Let f(x) = for x + 3. How should f(3) be defined so that f will be continuous (л — 3)…

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Q: (x + 1, x 0 Can also be displayed as: x + 1 when x 0 f(x) = Is f(x) continuous at x = 0? Why or why…

A: We have to find the solution of continuity