a)Suppose f: R → Z, where f(x) = [x + ¹] i. Graph the function f(x). ii. If A = {x: 1 ≤ x ≤ 3}, find f(A). iii. Find f-¹({0})
a)Suppose f: R → Z, where f(x) = [x + ¹] i. Graph the function f(x). ii. If A = {x: 1 ≤ x ≤ 3}, find f(A). iii. Find f-¹({0})
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![a)Suppose f: R → Z, where f(x) = [x + ¹]
i. Graph the function f(x).
ii. If A = {x: 1 ≤ x ≤ 3}, find f(A).
iii. Find f-¹({0})
iv. Find f¹({-1,0,1))
b) Let the functions f, g and h be defined as follows:
f:R Rf(x) = 4x - 3
→>>
g: RR; g(x) = x² + 1
h: RR;h(x) =
(1 if x ≥ 0
if x < 0
lo
Find the rules for the following functions:
i
fog
ii.
gof
iii. foh
iv. hof](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F026262b7-e0da-499f-ba7b-2292f994704c%2Fa64c7f72-af87-4c36-adad-572c082a3fb8%2F3gtxetm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a)Suppose f: R → Z, where f(x) = [x + ¹]
i. Graph the function f(x).
ii. If A = {x: 1 ≤ x ≤ 3}, find f(A).
iii. Find f-¹({0})
iv. Find f¹({-1,0,1))
b) Let the functions f, g and h be defined as follows:
f:R Rf(x) = 4x - 3
→>>
g: RR; g(x) = x² + 1
h: RR;h(x) =
(1 if x ≥ 0
if x < 0
lo
Find the rules for the following functions:
i
fog
ii.
gof
iii. foh
iv. hof
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