Question

Let f(x) = 2x^2 – 3, x > 3

a) Find the inverse of f(x) and label it g(x).
b) Find f '(x) and g'(x).
c) Find g'(15).
d) Find g(15).
d) Find f '(g(15)).
f) Write the reciprocal of your answer for part e.
Theorem 5.09 tells us that the answers to part c and part f must be equal. Use your knowledge of the relationship of the derivative of a function to the slope of the tangent line at a given point and your knowledge that for every point (x, y) on the graph of a function that has an inverse there is a corresponding point (y, x) on the inverse function to explain how we know that

Answer 1

how we know that g'(15) = \[\frac{ 1 }{ f'(g(15)) }\]

Answer 2

my replay overlays the last sentence in the initial question.