The function f(x) = e4x+x+3 is one-to-one for all x E R. We recall that the inverse function f(x) is defined such that y = f-1(x) if and only if x = f(y). Our goal is to find the equation of the tangent line to the curve y = f-1(x) at x = e. 1. We find the point of tangency. We need to find the y-coordinate of the point on the curve y = f(x) with x-coordinate x = e. That is, we need to find f-1 (e). We get: 1 (e) = 2. We find the slope of the tangent line to the curve y = f-1(x) at the point with x = e. The slope is given by: m = 3. Putting this together, we obtain the equation of the tangent line: y =