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 byf(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 → Rax + bis defined by f(x)cx + d1. 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.

Answered: Let a, b, c, d be real numbers where 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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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.

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