Let a, b, c, d be real numbers where c and d are not both zero. Let X = {x E R | cx + d + 0}. The function f :X → R ax + b is defined by f(x) cx + d 1. Under what condition/s on a, b, c, d will ƒ be one-to-one? 2. In addition to the condition/s above, justify that f is a bijection iff c = 0.
Let a, b, c, d be real numbers where c and d are not both zero. Let X = {x E R | cx + d + 0}. The function f :X → R ax + b is defined by f(x) cx + d 1. Under what condition/s on a, b, c, d will ƒ be one-to-one? 2. In addition to the condition/s above, justify that f is a bijection iff c = 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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Let a, b, c, d be real numbers where c and d are not both zero. Let X = {x is a real number | cx + d =/= 0}. The function f : X -> R is defined by
f(x) = (ac + b)/(cx + d)
a. Under what condition/s on a, b, c, d will f be one-to-one?
b. In addition to the condition/s above, justify that f is a bijection iff c = 0.
![Let a, b, c, d be real numbers where c and d are not both zero. Let X = {x E R | cx + d + 0}. The function f :X → R
ax + b
is defined by f(x)
cx + d
1. Under what condition/s on a, b, c, d will ƒ be one-to-one?
2. In addition to the condition/s above, justify that f is a bijection iff c = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F071ad70b-680b-44d6-b888-10a290f238d8%2Fe7eeb9e9-d48d-4a2c-8f26-cd3bb8428f57%2Ffmk3dzf_processed.png&w=3840&q=75)
Transcribed Image Text:Let a, b, c, d be real numbers where c and d are not both zero. Let X = {x E R | cx + d + 0}. The function f :X → R
ax + b
is defined by f(x)
cx + d
1. Under what condition/s on a, b, c, d will ƒ be one-to-one?
2. In addition to the condition/s above, justify that f is a bijection iff c = 0.
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