The differentiable function is strictly increasing on all real numbers and has…

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

The differentiable function

f

is strictly increasing on all real numbers and has inverse function

g=f^{-1}

. A point

P

on the graph of

f

(2,5)

, and the tangent line to

f

P

has slope

4

. (a) Describe the geometric relationship between the graphs of

f

and

g

with respect to the line

y=x

. (b) Using this relationship, determine the slope of the tangent line to the graph of

g

at the point

Q=(5,2)

and explain your reasoning without performing any symbolic differentiation.