Question 1187567

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

inverse:

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

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

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

{{{y=x/5}}}

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

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


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


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

={{{(5x)/5}}}

={{{x}}}