Question

Find the inverse of f(x)=e^2x-1

Answer 1

`f(x)=e^(2x-1)\\\\y=e^(2x-1)\\\\\text{replace x with y and y with x}\\\\x=e^(2y-1)\\\\\text{solve for y}\\\\e^(2y-1)=x\ \ \ \ |\ln\\\\\ln e^(2y-1)=\ln x\\\\2y-1=\ln x\ \ \ |+1\\\\2y=\ln x+1\ \ \ |:2\\\\y=(\ln x+1)/(2)\\\\Answer:\ \boxed{f^(-1)(x)=(\ln x+1)/(2),\ x > 0}`