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Calc AB

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)

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

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

    which would be 1/2x-4 correct?

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

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

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