Find the Inverse f(x) = square root of 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. Square both sides of the equation to eliminate the square root.

x^2=9−y^2

4. Isolate the y^2 term by subtracting 9 from both sides and multiplying by −1

y^2=9−x^2

5. Solve for y by taking the square root of both sides, noting that the domain of the original function restricts the range of the inverse.

y=√(,9−x^2)

6. Replace y with ƒ(x)^(−1) to state the final inverse function.

ƒ(x)^(−1)=√(,9−x^2)

Final Answer

ƒ(x)^(−1)=√(,9−x^2)

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