does this function exist?

Question

for the function Q(x) = 6e^0.04x does Q^-1 exist?

 

if yes find it and evaluate to 4 decimal places Q(9) and Q^-1(9) 

Answer 1

Yes; in general, the inverse of an exponential function is a logarithmic function.

 

Q(9) = 6e^0.36 = 8.6, approx.

 

Interchanging variables & solving for new "y" to get Q inverse:

x = 6e^0.04y

ln x = ln 6 + 0.04y

y = 25(ln x - ln 6) = Q^-1(x); now you go ahead and find Q^-1(9).