Consider the function f : [-1, √/10] → R defined by [x², X, f(x) 10 8 6 4 2 0 -1 f(x) = 0 1 1 x > 2; x ≤ 2. X I 2 3 4 Answer each of the following questions on the discontinuity of f. By using the e-8 definition, explain why limx→2 f(x) does not exist. Consider the set (0,5). Find the preimage f-¹((0,5)) and use the topologica characterization of continuous functions.
Consider the function f : [-1, √/10] → R defined by [x², X, f(x) 10 8 6 4 2 0 -1 f(x) = 0 1 1 x > 2; x ≤ 2. X I 2 3 4 Answer each of the following questions on the discontinuity of f. By using the e-8 definition, explain why limx→2 f(x) does not exist. Consider the set (0,5). Find the preimage f-¹((0,5)) and use the topologica characterization of continuous functions.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![Consider the function ƒ : [−1, √/10] → R defined by
[x²,
x,
f(x)
10
8
6
4
2
0
-1
ƒ(x) =
0
1
1
x > 2;
x ≤ 2.
X
I
2
3
4
Answer each of the following questions on the discontinuity of f.
By using the € - 8 definition, explain why limx→2 f(x) does not exist.
Consider the set (0,5). Find the preimage f-¹((0,5)) and use the topological
characterization of continuous functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26bcc706-1d6a-4c95-be9e-aef76f432780%2F3e5287af-1965-4aff-9d8e-cdd1326e55f6%2Fqsl8x4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the function ƒ : [−1, √/10] → R defined by
[x²,
x,
f(x)
10
8
6
4
2
0
-1
ƒ(x) =
0
1
1
x > 2;
x ≤ 2.
X
I
2
3
4
Answer each of the following questions on the discontinuity of f.
By using the € - 8 definition, explain why limx→2 f(x) does not exist.
Consider the set (0,5). Find the preimage f-¹((0,5)) and use the topological
characterization of continuous functions.
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