Question: Given the function​ f, find the slope of the line tangent to the graph of f^-1 at the specified point on the graph of f^−1.   f(x) = sqrt(5x)     ;     (4, 16/5)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question:

Given the function​ f, find the slope of the line tangent to the graph of

f^-1 at the specified point on the graph of f^−1.
 
f(x) = sqrt(5x)     ;     (4, 16/5)
 
 
My Comments: 
 
The way I'm solving this is taking the derivative, then flipping the fraction.  For the derivative, I got (5/2x)^-1/2.  Then I believe you swap the fraction to get the inverse function, but I'm not sure how to swap it with the -1/2 exponent.  (Assuming I even started this question correctly.)
Can you explain how to solve this?
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