Question

Find a formula for the inverse of the function: f(x) = 9–6/x^2, x>0.


f^-1(x)=

Answer 1

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Answer:

f^-1(x) = √(6/(9 -x))

Explanation:

The inverse function is the solution to ...

x = f(y)

x = 9 -6/y^2

x +6/y^2 = 9 . . . . . add 6/y^2

6/y^2 = 9 -x . . . . . subtract x

6/(9 -x) = y^2 . . . . . multiply by y^2/(9 -x)

y = √(6/(9 -x)) . . . . take the square root

Then the inverse function can be written as ...

f^-1(x) = √(6/(9 -x)) . . . . . . x < 9