Question 1187100


{{{k(x)=3x^2-5}}}

find inverse:

recall that

{{{k(x)=y}}}

{{{y=3x^2-5}}}.........swap variables

{{{x=3y^2-5}}}.........solve for{{{ y}}}

{{{x+5=3y^2}}}

{{{y^2=(x+5)/3}}}

{{{y=sqrt(x+5)/3)}}}

{{{ y}}}= ± {{{sqrt(x + 5)/sqrt(3)}}}

=> inverse is {{{k}}}'{{{(x)}}}= ± {{{sqrt(x + 5)/sqrt(3)}}}


A. {{{k}}} {{{has}}} an inverse function