SOLUTION: Show that the following functions are inverse functions: f(x)=(1/4)ln(x) g(x)=e^(4x) Thank you!

Algebra ->  Inverses -> SOLUTION: Show that the following functions are inverse functions: f(x)=(1/4)ln(x) g(x)=e^(4x) Thank you!      Log On


   

Question 1127080: Show that the following functions are inverse functions:
f(x)=(1/4)ln(x)
g(x)=e^(4x)
Thank you!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%281%2F4%29ln%28x%29
recall: f%28x%29=y
To find the inverse, interchange the variables and solve for y.
y=ln%28x%5E%281%2F4%29%29
x=ln%28y%5E%281%2F4%29%29
x=ln%28y%5E%281%2F4%29%29
x=ln%28y%29%2F4
4x=ln%28y%29
y=e%5E%284x%29 inverse
f%5E-1%28x%29=e%5E%284x%29 which is equal to g%28x%29=e%5E%284x%29