17 Prove that the function g(n) = 2n - 3 defined for al positive integers is one to one. Recall the definition of one to one function is for all numbers in the domain of g: n1,n2, if g(n-ginz), then n1=n2 Adding 3 to both sides of the equation, we get: 2n12 = 2n22 Therefore, g is a one to one function. Using definition of g, 2n12-3= 2n22-3 %3! dividing by 2 then taking square root of both sides and keeping in mind that n1,n2 are positive integers: n1 = n2 %3D Suppose that n1.n2 are positive integers such that g(n1)=g(n2)
17 Prove that the function g(n) = 2n - 3 defined for al positive integers is one to one. Recall the definition of one to one function is for all numbers in the domain of g: n1,n2, if g(n-ginz), then n1=n2 Adding 3 to both sides of the equation, we get: 2n12 = 2n22 Therefore, g is a one to one function. Using definition of g, 2n12-3= 2n22-3 %3! dividing by 2 then taking square root of both sides and keeping in mind that n1,n2 are positive integers: n1 = n2 %3D Suppose that n1.n2 are positive integers such that g(n1)=g(n2)
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:17
Prove that the function g(n) = 2n - 3 defined for al positive integers is one to one.
Recall the definition of one to one function is
for all numbers in the domain of g: n1,n2, if g(n-g(nz), then n1=n2
Adding 3 to both sides of the equation, we get:
2n12 = 2n22
Therefore, g is a one to one function.
Using definition of g,
2n12-3= 2n22- 3
%3D
dividing by 2 then taking square root of both sides and keeping in mind that n1,n2 are positive integers:
n1 = n2
%3D
Suppose that n1.n2 are positive integers such that g(n1)=g(n2)
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