Question

Calculator question: Let f(x)=ln(e^2x)/(x-1) for x>1. If g is the inverse of f, then g'(3)=
(A) 2 (B) 1 (C) 0 (D)-1 (E)-2

Answer 1

1

Answer 2

the answer is -2, I just don't know how to get there

Answer 3

f(x) =ln(e^2x)/(x-1) First I can put the 2x up front.
f(x) = 2xln(e)/(x-1) Ln(e) = 1
f(x) = 2x/(x-1)

y = 2x/(x-1) Now to get the inverse.
x = 2y/(y-1)
xy - x = 2y
xy - 2y = x
y(x-2) = x
y = x/(x-2)

f'(x) = [(x-2) - x]/(x-2)^2
f'(x) = -2/(x-2)^2

f'(3) = -2/(3-2)^2
f'(3) = -2/1^2
f'(3) = -2