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sp2606 [1]
2 years ago
8

Find a formula for the inverse of the function: f(x) = 9–6/x^2, x>0. f^-1(x)=

Mathematics
1 answer:
QveST [7]2 years ago
5 0

9514 1404 393

Answer:

  f^-1(x) = √(6/(9 -x))

Step-by-step 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

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