Question 54968
Find the Inverse of the following function:
:
{{{f(x)=10^(x-3)+4}}}
{{{y=10^(x-3)+4}}}  Switch the x and y and solve for y.
{{{x=10^(y-3)+4}}}
{{{x-4=10^(y-3)+4-4}}}
{{{x-4=10^(y-3)}}}  Take the log of both sides:
{{{log((x-4))=log((10^(y-3)))}}}
{{{log((x-4))=(y-3)log(10)}}}  Note the common log of 10=1
{{{log((x-4))=(y-3)(1)}}}
{{{log((x-4))=y-3}}}
{{{log((x-4))+3=y-3+3}}}
{{{log((x-4))+3=y}}} Replace y with f^-1(x)
{{{f^(-1)(x)=log((x-4))+3}}}
Happy Calculating!!!