Question 1136442

For each of the following functions, write the formula for the function's inverse. 
a.) 

{{{f(x)=4(2.6)^x }}}where {{{y=f(x)}}}

{{{y=4(2.6)^x }}}....swap {{{x}}} and {{{y}}}

{{{x=4(2.6)^y }}}....solve or {{{y}}}

{{{x/4=(2.6)^y }}}.....take log of both sides

{{{log(x/4)=log((2.6)^y) }}}

{{{log(x/4)=ylog(2.6) }}}

{{{y=log((x/4))/log((2.6))}}}

{{{f^-1(x)=log((x/4))/log((2.6))}}}





b.) 

{{{f(x)=log(10,(x/21))}}} where {{{y=f(x)}}}

{{{y=log(10,(x/21))}}}

{{{x=log(10,(y/21))}}}....recall that {{{log(b,(y) )= x}}} is equivalent to (means the exact same thing as) {{{y = b^x}}}

{{{y /21= 10^x}}}

{{{y=21*10^x}}}

{{{f^-1(x)=21*10^x}}}