Find the Inverse f(x)=9/(x^2)

Problem

ƒ(x)=9/(x^2)

Solution

1. Replace ƒ(x) with y to set up the equation for the inverse.

y=9/(x^2)

2. Swap the variables x and y to begin solving for the inverse function.

x=9/(y^2)

3. Multiply both sides by y^2 to move the variable out of the denominator.

x*y^2=9

4. Divide both sides by x to isolate the y^2 term.

y^2=9/x

5. Take the square root of both sides to solve for y

y=±√(,9/x)

6. Simplify the square root by taking the root of the numerator.

y=±3/√(,x)

7. Replace y with ƒ(x)^(−1) to denote the inverse function.

ƒ(x)^(−1)=±3/√(,x)

Final Answer

ƒ(x)^(−1)=±3/√(,x)

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