Question 1187800


{{{f(x)=(x-7)/4}}}

find
{{{f^-1(x)}}}=

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

{{{y=(x-7)/4}}}........swap variables

{{{x=(y-7)/4}}}...........solve for{{{ y}}}

{{{4x=y-7}}}

{{{4x+7=y }}}

so,

{{{f^-1(x)=4x+7}}}


verify

{{{f(f^-1(x))=x}}}

{{{f(f^-1(x))=f(4x+7)}}}

{{{f(f^-1(x))= ((4x+7)-7)/4}}}

{{{f(f^-1(x))= (4x+7-7)/4}}}

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

{{{f(f^-1(x))= x}}}


verify

{{{f^-1(f(x))=x}}}

{{{f^-1(f(x))=f^-1((x-7)/4)}}}

{{{f^-1(f(x))=4((x-7)/4)+7}}}

{{{f^-1(f(x))=x-7+7}}}

{{{f^-1(f(x))=x }}}