SOLUTION: Find f^−1(x)for f(x)=23/x^2,x>0.

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Question 1188984: Find f^−1(x)for f(x)=23/x^2,x>0.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) A standard algebraic method for finding the inverse of a function: switch the variables and solve for the new y.

Given: y=23%2Fx%5E2

Switch variables:

x=23%2Fy%5E2

Solve for y:

y%5E2=23%2Fx
y=sqrt%2823%2Fx%29

(2) An informal method, using the idea that an inverse function "un-does" what the function does.

The given function does the following to the input:

square it; take the reciprocal; multiply by 23

x --> x%5E2 --> 1%2Fx%5E2 --> 23%2Fx%5E2

The inverse function must do the opposite operations, in the opposite order:

divide by 23; take the reciprocal; take the square root

x --> x%2F23 --> 23%2Fx --> sqrt%2823%2Fx%29