Let f ( x ) = x + e x {\displaystyle f(x)=x+e^{x}} . Find the equation of the tangent line of y = f − 1 ( x ) {\displaystyle y=f^{-1}(x)} at x = 1 {\displaystyle x=1} . Recall that f − 1 ( x ) {\displaystyle f^{-1}(x)} is the inverse function of f ( x ) {\displaystyle f(x)} and its derivative can be calculated using formula d f − 1 d x = 1 f ′ ( f − 1 ( x ) ) {\displaystyle {\frac {df^{-1}}{dx}}={\frac {1}{f'(f^{-1}(x))}}} .
