Question 1196625
Find a formula for the inverse of the function.

{{{y = e^(4 -x)}}}

to find inverse swap the variables

{{{x= e^(4 -y)}}}..........solve for {{{y}}}, take natural logarithm of bot sides

{{{ln(x)=ln( e^(4 -y))}}}

{{{ln(x)=(4 -y)ln( e)}}}..............{{{ln( e)=1}}}

{{{ln(x)=4 -y}}}

{{{y=4 -ln(x)}}}

{{{f^-1(x)=4 -ln(x)}}}-> inverse


{{{ drawing( 600, 600, -10, 10, -10, 10, locate(1,4,4 -ln(x)), locate(4,2,e^(4 -x)),
graph( 600, 600, -10, 10, -10, 10, e^(4 -x), 4 -ln(x)) )}}}