Answer to Question #330059 in Discrete Mathematics for erroll

Question

Determine whether each of these functions from Z to Z is one-to-one.

a) f(x) = x−2

b) f(x) = x2 −1

c) f(x) = x3

Answer 1

$a:\\f\left( x \right) =f\left( y \right) \Rightarrow x-2=y-2\Rightarrow x=y\,\,-\,\,yes\\b:\\f\left( 1 \right) =1^2-1=0\\f\left( -1 \right) =\left( -1 \right) ^2-1=0\\f\left( 1 \right) =f\left( -1 \right) \,\,-\,\,no\\c:\\f\left( x \right) =f\left( y \right) \Rightarrow x^3=y^3\Rightarrow x=y\,\,-\,\,yes$