Question

Suppose that y = f(x) = x^2-4x+4

Then on any interval where the inverse function y = f^–1(x) exists, the derivative of y = f^–1(x) with respect to x is:

a) 1/(2x-4)
b) 1/(2y-4), where x and y satisfy the equation y=x^2-4x+4
c)(1/2)x^(-1/2)
d)(1/2)x^(1/2)
e) Both 1/(2y-4), where x and y satisfy the equation y=x^2-4x+4 and (1/2)x^(-1/2)

Answer 1

Hint: dx/dy = 1/(dy/dx)

Answer 2

That would be 1/(dy/dx) of x^2-4x+4

which would be 1/2x-4 correct?

Answer 3

Wait f^-1(x) is 2sqrt(x) so then the derivative of that is 1/sqrt(x)

Answer 4

c)(1/2)x^(-1/2) is the correct answer

Answer 5

f(x) = x^2-4x+4
y = (x-2)^2
Inverse function
x = (y-2)^2
Differentiate the inverse function, you would get
y' = 1/(2sqrt(x))