Question 1194819


given: {{{f(x) = x^3}}}


To show that a function is {{{injective}}}, we assume that there are elements {{{a}}} and {{{b}}} of a domain with {{{f(a) = f(b)}}} and then show that {{{a = b}}}.


{{{f(a)=f(b)}}}

{{{f(a)=a^3 }}}

{{{f(b)=b^3 }}}

{{{a^3=b^3}}}  take the cubic root of each side

{{{a=b}}}

Therefore, {{{f}}} is {{{injective}}}.