Let n be a positive integer and let f : [0..n] → [0..n] be an injective function. Define the function g: [0..n] → Z as g(x) = n(f(x))². Prove that g is also injective.
Let n be a positive integer and let f : [0..n] → [0..n] be an injective function. Define the function g: [0..n] → Z as g(x) = n(f(x))². Prove that g is also injective.
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 n be a positive integer and let f : [0..n] → [0..n] be an injective function. Define the function
g: [0..n] → Z as g(x) = n − (f(x))². Prove that g is also injective.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac0fe233-9215-469b-9b52-607d6dc120fe%2F65eb07c8-ea62-4c88-97ae-edcb83c8d478%2Fz5ej0r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let n be a positive integer and let f : [0..n] → [0..n] be an injective function. Define the function
g: [0..n] → Z as g(x) = n − (f(x))². Prove that g is also injective.
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