Question 1069474
The reciprocal, or inverse function, is found by first solving y = 4e^x/(3+5e^x) for x.  You should obtain the following equation.  x = ln(3y/(4-5y))
Now reverse x and y:
y = ln(3x/(4-5x)) = f_inv(x)
If we plot the two functions, we see that they are reflections of each other about the line y=x:
{{{graph(300,300,-6,10,-8,10,4*exp(x)/(3+5*exp(x)),ln(3*x/(4-5*x)),x)}}}