f:Z → Z, f (m) 3 Зт - 2 g: R → S, where S = g(x) = |x| {x € R]x 2 0} h: R* → R, h(x) = In(x) R*is a set of positive real numbers r:Z → Z, r(n) : p: Q → Q, p(x) = x + 3 u: R → R, u(x) = x² Select one function from the list above and determine whether the function is a one-to-one function, onto function, and bijection. Prove all your answers.

f:Z → Z, f (m) 3 Зт - 2 g: R → S, where S = g(x) = |x| {x € R]x 2 0} h: R* → R, h(x) = In(x) R*is a set of positive real numbers r:Z → Z, r(n) : p: Q → Q, p(x) = x + 3 u: R → R, u(x) = x² Select one function from the list above and determine whether the function is a one-to-one function, onto function, and bijection. Prove all your answers.

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

f:Z → Z,
%3D
g(x) = |x|
g:R → S,
where S = {x E R|x 2 0}
%3D
h(x) = In(x)
R*is a set of positive real numbers
h: R* → R,
[n'
r:Z → Z,
r(n) =
p: Q → Q,
p(x) = x + 3
u: R → R,
u(x) = x²
Select one function from the list above and determine whether the function is a one-to-one function, onto
function, and bijection. Prove all your answers.

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