For all suitable real numbers x, define f(x) = 1 √x² - 4x + 5 [Hint: Complete the square!] (a) Find the domain of f. (b) Give an example to show that f is not an injection. Describe the range of f. (c)
For all suitable real numbers x, define f(x) = 1 √x² - 4x + 5 [Hint: Complete the square!] (a) Find the domain of f. (b) Give an example to show that f is not an injection. Describe the range of f. (c)
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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![(5) For all suitable real numbers x, define
f(x) =
1
√x² - 4x + 5*
[Hint: Complete the square!]
(a)
Find the domain of f.
(b)
Give an example to show that f is not an injection.
Describe the range of f.
(c)
(d)
Justify your answer in (d).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0a394bc-2c1f-41f1-b964-e2df9d0d082c%2F6a4bb79c-b6df-4330-8449-6368d1ad1f2f%2Fnv657fc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(5) For all suitable real numbers x, define
f(x) =
1
√x² - 4x + 5*
[Hint: Complete the square!]
(a)
Find the domain of f.
(b)
Give an example to show that f is not an injection.
Describe the range of f.
(c)
(d)
Justify your answer in (d).
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