Question 1187566


{{{f(x)=5x+4}}}

inverse:

{{{f(x)=y}}}

{{{y=5x+4}}}...............swap variables

{{{x=5y+4}}}...........solve for {{{y}}}

{{{x-4=5y}}}
{{{y=(x-4)/5}}}

{{{f^-1(x)=(x-4)/5}}}

verify that {{{f(f^-1(x))=x}}} and {{{f^-1(f(x))=x}}}


{{{f(f^-1(x))=f((x-4)/5)}}}
={{{5((x-4)/5)+4}}}.....simplify
={{{x-4+4}}}
={{{x}}}


{{{f^-1(f(x))=f^-1(5x+4)}}}

={{{(5x+4-4)/5 }}}
={{{(5x)/5 }}}
={{{x}}}