For the function f(x) = sqrt(9-x), which is equal to d/dx(f-1( -1 is the inverse)(x))

a) -2x
b) sqrt(x) + 9
c) x^2 + 9
d) 2x
e) 9-x^2

5 answers

well, f^-1(x) = 9-x^2, so ...

well lets see. Since f^-1(x) = 9-x^2 then the derivative of 9-x^2 is -2x correct?

Yep I was correct

-2x

The inverse function is x = sqrt(9-y)
If you differentiate the inverse function, you would get
y' = -2 * sqrt(9-y)
Then substitue x = sqrt(9-y)
y' = -2x

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