If f(x)= ln(x) + arctan(x) ; find (f^-1)'(pi/4)

Question

Please help me with all the steps! 

Answer 1

This type of problem usually requires a numerical (calculator) solution. 

 

However, this case is easy.      We want to find the value of x such that

 

ln(x) + arctan(x) =   π/4.

 

Start by remembering that tan(π/4) = 1    (i.e. the tangent of 45° is 1).     So arctan(1 ) = π/4

 

Now if the ln(1) were zero, we would be done.    But , in fact,  ln(1) does equal zero!

 

So the final answer is   x = 1.