Let F and G be differentiable functions such that g(x)= f^-1(x). If f(2)=4, f(3)=9, g’(4)=1/4, and g’(9)=1/6, what is the value of f’(3)

Question

Multiple choice answers are

a.) 0

b.) 3

c.) 4

d.) 6

e.) 9

Answer 1

Since f(3) = 9, f^-1(9) = g(9) = 3

f'(3), which is the slope of the tangent to the graph of y = f(x) at the point (3,9), is the reciprocal of the slope of the tangent to the graph of y = f^-1(x) at the point (9,3).

So, f'(3) = 1 / g'(9) = 1 / (1/6) = 6