Question #330059

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



1
Expert's answer
2022-04-18T15:54:29-0400

a:f(x)=f(y)x2=y2x=yyesb:f(1)=121=0f(1)=(1)21=0f(1)=f(1)noc:f(x)=f(y)x3=y3x=yyesa:\\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


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